Write a matrix that when multiplied by any point [x/y] would have the effect of rotating the point 90 degrees counterclockwise. Also determine the algebraic effect of performing the transformation on the point A.
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The result of rotating the point [-5, 2] by 90 degrees counterclockwise is the point [2, -5].
Define rotationRotation is a transformation in geometry that involves turning or spinning an object around a fixed point called the center of rotation. The center of rotation remains stationary while all the points of the object move along circular paths, at the same angle and distance from the center.
To rotate a point [x/y] counterclockwise by 90 degrees, we can use a 2x2 matrix of the form:
[ 0 -1 ]
[ 1 0 ]
To multiply this matrix by a point [x/y], we can use the following matrix multiplication:
[ 0 -1 ] [ x ] [ -y ]
[ 1 0 ] [ y ] = [ x ]
So, if we have a point [x/y] and we want to rotate it 90 degrees counterclockwise, we can multiply it by the matrix [ 0 -1 ; 1 0 ] to get the new point [-y/x].
To rotate a point 90 degrees counterclockwise using a matrix, we need to represent the point as a column matrix and then multiply it by the 2x2 rotation matrix.
Assuming that the point is [x, y] = [-5, 2], we can represent it as a column matrix:
| -5 |
| 2 |
To rotate the point counterclockwise by 90 degrees, we can use the following 2x2 rotation matrix:
| 0 -1 |
| 1 0 |
Multiplying the rotation matrix by the column matrix representing the point gives:
| 0 -1 | | -5 | | 2 |
| 1 0 | ×| 2 | = | -5 |
So the result of rotating the point [-5, 2] by 90 degrees counterclockwise is the point [2, -5].
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Related Questions
margo has 6 square tiles of equal size. each side of each tile is 0.8 inch long. if margi places all the tiles in a row with sides touching, how long is the row?
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—————————————————
Margi has 6 square tiles of equal size. each side of each tile is 0.8 inch long. If Margi places all the tiles in a row with sides touching, how long is the row?
༆SOLUTION:—————————————————
\(\mathrm{N = 6×0.8 \: inch}\)
\({\boxed{\mathrm\green{N = 4.8 \: inch}}}\)
༆ANSWER:—————————————————
\(\purple{\boxed{\boxed{\tt\pink{➢4.8 \: inch}}}}\)
If Margi places all the tiles in a row with sides touching, the row will be 4.8 inch long!For two programs at a university, the type
of student for two majors is as follows.
History Science
Total
390
422
812
73
261
463
1073
Find the probability a student is a graduate
student, given they are a history major.
P(graduate history) =
P(graduate and history)
P(history)
= [?]
Round to the nearest hundredth.
Undergraduate
Graduate
Total
188
610
Enter
Answers
The probability that a student is a graduate student, given that they are a history major, is given as follows:
0.1577 = 15.77%.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
There are 463 history students, and of those, 73 are graduate students, hence the probability is given as follows:
73/463 = 0.1577 = 15.77%.
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Can someone please help me
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Using Pythagorean theorem
\(\\ \sf\longmapsto P^2=H^2-B^2\)
\(\\ \sf\longmapsto P^2=6^2-5^2\)
\(\\ \sf\longmapsto P^2=36-25\)
\(\\ \sf\longmapsto P^2=11\)
\(\\ \sf\longmapsto P=3.2\)
_________
\( \: \)
a² = c² - b²
a² = 6² - 25²
a² = 36 - 25
a² = 11
a = √11
a ≈ 3.2
Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line
point = (-2, 3, 5)
Answers
The parametric equations and symmetric equations of the line are:
(x, y, z) = (-2, 3, 5) + t(u, v, w)
(x + 2) / u = (y - 3) / v = (z - 5) / w
Let's first consider the case where the line is parallel to a given vector.
If the line is parallel to a vector v = (a, b, c), then any point on the line can be represented as:
(x, y, z) = (x₀, y₀, z₀) + t(a, b, c)
where (x₀, y₀, z₀) is a point on the line and t is a parameter that varies over all real numbers.
Now, suppose we want the line to pass through a point P = (-2, 3, 5) and be parallel to a vector v = (u, v, w). Then we can choose P as our point on the line and write:
(x, y, z) = (-2, 3, 5) + t(u, v, w)
These are the parametric equations of the line.
To find the symmetric equations of the line, we can eliminate the parameter t by solving for it in each equation:
x + 2 = tu
y - 3 = tv
z - 5 = tw
Then, we can eliminate t by setting the ratios of these equations equal to each other:
(x + 2) / u = (y - 3) / v = (z - 5) / w
These are the symmetric equations of the line.
Alternatively, if the line is parallel to another line L that passes through a point Q = (x₁, y₁, z₁) and has direction vector d = (d₁, d₂, d₃), then any point on the line can be represented as:
(x, y, z) = (x₁, y₁, z₁) + t(d₁, d₂, d₃)
where t is a parameter that varies over all real numbers.
To find the parametric equations and symmetric equations of the line that passes through P and is parallel to L, we can set Q = P and d = v, giving:
(x, y, z) = (-2, 3, 5) + t(u, v, w)
(x + 2) / u = (y - 3) / v = (z - 5) / w
These are the parametric equations and symmetric equations of the line.
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EXPERTS OR ACES PLEASE ANSWER THIS FAST DUE IN 2 MIN 50 POINTS
Answers
Answer:
24 blocks
Step-by-step explanation:
b = 2(9) + 6b = 18 + 6b = 24iv. What is the statement of Fick's First law? Express also, in mathematical form. Identify and explain the parameters in your equation. What is the statement of Fick's second law, in mathematical form? Identify and explain the parameters in your equation.
Answers
Fick's First law of diffusion states that the rate of diffusion of a substance is directly proportional to the concentration gradient of the substance.Fick's Second law of diffusion states that the rate of change of concentration of a substance with time is proportional to the rate of the movement of the substance by diffusion.
Fick's First law of diffusion
Fick's First law of diffusion states that the rate of diffusion of a substance is directly proportional to the concentration gradient of the substance. The mathematical equation for Fick's First Law is given as follows:
J = - D(dC/dx),
where J represents the flux of the diffusing species, dC/dx is the concentration gradient, and D is the diffusion coefficient.
The parameter dC/dx refers to the concentration gradient that exists between two points and is the change in concentration of a substance over a distance. This parameter helps in determining the movement of a substance from higher concentration to lower concentration.
Fick's Second law of diffusion
Fick's Second law of diffusion states that the rate of change of concentration of a substance with time is proportional to the rate of the movement of the substance by diffusion.
The mathematical equation for Fick's Second Law is given as follows:
∂C/∂t = D(∂2C/∂x2),
where C is the concentration of the diffusing species, t is the time, x is the distance, and D is the diffusion coefficient.
The parameter ∂C/∂t refers to the rate of change of concentration with time, while ∂2C/∂x2 refers to the rate of change of concentration with distance. These parameters are important in determining the rate of diffusion of a substance in a given system.
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AC−⇀− bisects ∠BAD.If m∠BAC=38°, find the m∠BAD.
Answers
Answer:
180-38=142 the other angle is 142
Step-by-step explanation:
Helppppppppppppppppp plzzzzzzzzzzzzzzzzzzzzzz
Answers
In a certain population, 27% of individuals are overweight. If
100 individuals are chosen at random, what is the standard
deviation of the number of individuals expected to be
overweight?
Answers
The standard deviation of the number of individuals expected to be overweight, out of a random sample of 100 individuals from the population, is approximately 4.305.
The standard deviation of the number of individuals expected to be overweight, out of a random sample of 100 individuals from a population where 27% are overweight, can be calculated using the formula for the standard deviation of a binomial distribution, which is the square root of the product of the sample size, the probability of success, and the probability of failure.
In this case, the probability of success is 27% or 0.27 (the proportion of individuals in the population who are overweight), and the probability of failure is 1 minus the probability of success, which is 1 - 0.27 = 0.73. The sample size is 100.
The formula for the standard deviation of a binomial distribution is given by:
σ = √(n * p * q)
where σ is the standard deviation, n is the sample size, p is the probability of success, and q is the probability of failure.
Plugging in the values, we have:
σ = √(100 * 0.27 * 0.73) ≈ 4.305
Therefore, the standard deviation of the number of individuals expected to be overweight, out of a random sample of 100 individuals from the population, is approximately 4.305.
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The green iguana got its name because of its green skin. the green iguana probably lives?
Answers
Answer:
The Green Iguana is native to South & Central America, Mexico, and some islands of the Caribbean and lives in the jungle.
Step-by-step explanation:
what's the ratio of 80:70
Answers
Answer:
8:7
Step-by-step explanation:
If you simplify 80/70 by 10,
80/10 = 8
70/10 = 7
you would get 8/7
Answer:
80:70 will be equals 8:7 divide to the lowest
Karen works for a cell phone company. If she's service the first 50 customers that Came To the store to find out if they would buy a new cell phone today if it cost $75. Out of the 50 customer survey, 22 of them stated that they would buy it if 200 customers came to that cell phone company that day which of the following would be the best prediction of how many would purchase that phone
44 customers
88 customers
108 customers
454 customers
Answers
Answer:
Dear Karen, I am the manager. You are now banned from Starbucks.
Step-by-step explanation:
108 customers
Look at the steps and find the pattern. Step one has 6 step two has 14 step three has 21 how many dots are in the 5th step
Answers
As per the details given, there are 37 dots in the 5th step.
To locate the pattern and decide the range of dots in the 5th step, allow's examine the given records:
Step 1: 6 dots
Step 2: 14 dots
Step 3: 21 dots
Looking on the variations between consecutive steps, we will see that the quantity of additional dots in each step is growing via eight.
In other phrases, the distinction among Step 1 and Step 2 is eight, and the difference between Step 2 and Step 3 is likewise eight.
Thus, we can preserve this sample to decide the quantity of dots within the 4th and 5th steps:
Step 4: 21 + 8 = 29 dots
Step 5: 29 + 8 = 37 dots
Therefore, there are 37 dots in the 5th step.
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This one is definitely tricky
Answers
The tangent of 15º is given as follows:
\(\tan{15^\circ} = = \frac{2 - \sqrt{3}}{2}\)
How to calculate the tangent of 15º?The double angle measure to 15º is given as follows:
30º.
The half angle theorem for the tangent is given as follows:
tan(x/2) = (1 - cos(x))/sin(x).
At x = 30º, the sine and the cosine are given as follows:
sin(x) = 1/2.\(\cos{x} = \frac{\sqrt{3}}{2}\)Hence the numerator is given as follows:
\(1 - \frac{\sqrt{3}}{2} = \frac{2 - \sqrt{3}}{2}\)
For the fraction, the numerator is multiplied by the inverse of the denominator, hence we simplify the 2 terms and the tangent is given as follows:
\(\tan{15^\circ} = = \frac{2 - \sqrt{3}}{2}\)
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8+10p=12+10p-4
Help me please
Answers
Answer:
p=0
Step-by-step explanation:
subtract 10p from both sides that leaves 8+p=12-4 12-8=4 p=4-4 p=0
Which sequence could be partially defined by the recursive formula.
Answers
A sequence that can be partially defined by a recursive formula is one where each term is determined based on the previous terms.
A recursive formula is a mathematical expression that describes a sequence by relating each term to one or more previous terms. It allows us to generate subsequent terms in the sequence based on the values of earlier terms. The recursive formula typically consists of two components: a base case that defines the initial term(s) of the sequence, and a recursive rule that expresses how to calculate each subsequent term based on the previous term(s).
For example, let's consider a sequence defined by the recursive formula: a(n) = a(n-1) + 3, with a(0) = 1. In this case, the base case is a(0) = 1, which specifies the initial term of the sequence. The recursive rule a(n) = a(n-1) + 3 states that each term is obtained by adding 3 to the previous term. Starting from a(0) = 1, we can calculate subsequent terms as follows: a(1) = a(0) + 3 = 1 + 3 = 4, a(2) = a(1) + 3 = 4 + 3 = 7, and so on.
In summary, a sequence partially defined by a recursive formula allows us to generate terms by using a rule that depends on the previous terms. It provides a systematic way to calculate subsequent values and explore the pattern or behavior of the sequence.
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ronald lau, chief engineer at south dakota electronics, has to decide whether to build a new state-of-the-art processing facility. if the new facility works, the company could realize a profit of $200,000. if it fails, south dakota electronics could lose $190,000. at this time, lau estimates a 50% chance that the new process will fail. the other option is to build a pilot plant and then decide whether to build a complete facility. the pilot plant would cost $5,000 to build. lau estimates a 60% chance that the pilot plant will work. if the pilot plant works, there is a 75% probability that the complete plant, if it is built, will also work. if the pilot plant does not work, there is only a 30% chance that the complete project (if it is constructed) will work. lau faces a dilemma. by analyzing this problem, help lau to maximize his expected payoff. what is the best decision you recommend for lau and what is the expected payoff? write your answer in the space below
Answers
I recommend that Ronald Lau build the pilot plant first to maximize his expected payoff. The expected payoff for this decision is $55,000.
To help Ronald Lau maximize his expected payoff, we can use decision analysis to evaluate the potential outcomes and probabilities of each decision.
The first decision is whether to build the new facility directly or to build the pilot plant first and then decide whether to build the complete facility.
If the new facility is built directly, the expected payoff is $200,000 × 0.5 + (-$190,000) × 0.5 = $5,000.
If the pilot plant is built first, the expected payoff is:
$5,000 + $200,000 × 0.75 × 0.6 + (-$190,000) × 0.25 × 0.6 = $55,000
or
$5,000 + (-$190,000) × 0.75 × 0.4 + $200,000 × 0.25 × 0.4 = -$45,000
The best decision is to build the pilot plant first since this decision has a higher expected payoff of $55,000 compared to the expected payoff of $5,000 for building the new facility directly.
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Find the value of x.
Answers
Answer:
x = 17.5
Step-by-step explanation:
the segment inside the triangle is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, so
\(\frac{7}{4}\) = \(\frac{x}{10}\) ( cross- multiply )
4x = 70 ( divide both sides by 4 )
x = 17.5
A bottle contains 255 coins 1/3 of the coins are £1 coins 110 of the coins are 50p coins the rest of the coins are 20p coins work out the total value of the coins contained in the bottle.
Answers
Answer:
£169
Step-by-step explanation:
255/3 = £85
110 x 50 p = 5500 p
255 - 110 = 145 coins which are 20 p
145 x 20 p = 2900 p
5500 p = £55
2900 p = £29
£85 + £55 + £29 = £169
Answer:
I sun 169 ofc
Step-by-step explanation:
What is m∠A?
Enter your answer in the box.
Answers
Answer:
60 degrees
Step-by-step explanation:
sum of interior angles in a triangle is always 180 degrees
find m<E from triangle CED: 43 + m<E + 35 = 180 degrees
m<E = 102 degrees
find m<A: 102 + m<A + 18 = 180
m<A = 60 degrees
3x+2= x - 3
I need help with this!!
Answers
Answer:
x =-(5/2)
Step-by-step explanation:
\(3x+2= x - 3\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\3x+2-2=x-3-2\\\\Simplify\\3x=x-5\\\\\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}\\3x-x=x-5-x\\\\Simplify\\2x=-5\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\frac{2x}{2}=\frac{-5}{2}\\\\Simplify\\x=-\frac{5}{2}\)
Can someone please help me ?
Answers
Answer:
yes3244
Step-by-step explanation:
i will help 5642
Please help me with this!
Answers
Step-by-step explanation:
step by step explaination is in the photo and the final answer is =
Two point charges (Q_(1))=9.00\times 10^(-9)C,Q_(2)=(-33\times 10^(-9)C) are separated by a distance of r=0.800m. What is the magnitude of the electric field at the midpoint between these charges, in units of ( N)/(C)?
Answers
The magnitude of the electric field at the midpoint between the charges can be calculated using the formula: E = k * (|Q₁| + |Q₂|) / (2 * r²), where k is the electrostatic constant. Plugging in the given values, we can find the magnitude of the electric field.
The electric field at a point due to a point charge is defined as the force experienced by a positive test charge placed at that point. It is a vector quantity with both magnitude and direction.
To calculate the electric field at the midpoint between the charges, we can consider the charges as two sources of electric field. The electric field due to each charge will have a magnitude and direction. At the midpoint, the electric fields due to both charges will have the same magnitude and direction.
The formula to calculate the electric field at the midpoint is given by E = k * (|Q₁| + |Q₂|) / (2 * r²), where k is the electrostatic constant (k ≈ 9 × 10^9 Nm²/C²), Q₁ and Q₂ are the magnitudes of the charges, and r is the distance between the charges.
By plugging in the given values (Q₁ = 9.00 × 10^(-9) C, Q₂ = -33 × 10^(-9) C, and r = 0.800 m) into the formula, we can calculate the magnitude of the electric field at the midpoint in units of (N/C).
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Can someone please help me with this question?
Answers
Answer:
Can someone please help me with this question?
Step-by-step explanation:
4x + 16 less than or equal to 18
Answers
4x = 18-16
x =2/4
x = 1/2
Answer:
x≤1/2
Step-by-step explanation:
4x+16 ≤18
Subtract 16 from each side
4x+16-16 ≤18-16
4x≤2
Divide by 4
4x/4 ≤2/4
x≤1/2
a basket contains $7$ green marbles and $5$ red marbles. a marble is taken from the basket at random; its color is recorded, then the marble is returned to the basket. a second marble is then taken from the basket at random, and its color is recorded. what is the probability that the same color is recorded both times?
Answers
35/864 is the probability that the same color is recorded both times .
How does probability explain work?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.7/12*1/2 = 7/24
red marbles = 5/12*1/3 ⇒ 5/36
the probability = 7/24*5/36 ⇒ 35/864
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the current world population is about 7.3 billion. under current conditions, the population is growing exponentially with a yearly growth factor of 1.011. in parts (b) and (c), round your answers to the nearest year. (a) find a formula that gives the world population n, in billions, after t years. n(t)
Answers
The current world population right now is over 8 billion.
If the graph shows (3, 1) what is the constant of proportionality 
Answers
Answer:
The constant of proportionality is 1/3Step-by-step explanation:
Proportional relationship equation:
y = kx, where k - constant of proportionalityUse the given point (3, 1) to find the value of k:
1 = 3kk = 1/3Answer:
k = 1/3
Step-by-step explanation:
Now we have to,
→ find the constant of proportionality.
Formula we use,
→ y = kx
The constant of proportionality is,
→ y = kx
→ 1 = k × 3
→ 3k = 1
→ [ k = 1/3 ]
Hence, required answer is 1/3.
For the system of differential equations x'(t) = -9/5 x + 5/3 y + 2xy y' (t) = - 18/5 x + 20/3 y - xy the critical point (x_0, y_0) with x_0 > 0, y_0 >, y_0 > is x_0 = 2/3 y_0 = 2/5 Change variables in the system by letting x(t) = x_0 + u(t), y(t) = y_o + v(t). The system for u, v is Use u and v for the two functions, rather than u(t) and v(t) For the n, v system, the Jacobean matrix at the origin is A = -1 3 -4 6 You should note that this matrix is the same as J(x_0, y_0) from the previous problem.
Answers
The system of differential equations after the change of variables is given by u'(t) = -3/5 u + 2/3 v + (4/9)x_0v + 4/15 u^2 + 4/15 uv and v'(t) = -4v + 6u + (8/3)x_0u - (2/3)y_0 - 2uv, with the Jacobian matrix A = [-1, 3; -4, 6] at the origin.
How to find Jacobian matrix?The given system of differential equations:
x'(t) = -9/5 x + 5/3 y + 2xy
y'(t) = -18/5 x + 20/3 y - xy
Critical point:
x_0 = 2/3, y_0 = 2/5
New variables:
x(t) = x_0 + u
y(t) = y_0 + v
New system of differential equations in terms of u and v:
u'(t) = -3/5 u + 2/3 v + (4/9)x_0v + 4/15 u^2 + 4/15 uv
v'(t) = -4v + 6u + (8/3)x_0u - (2/3)y_0 - 2uv
Jacobian matrix at the origin:
A = [-1, 3; -4, 6]
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