What is the answer to this?<br><br> What are the 2 equations for this?

To every linear transformation T from R2 to R2, there is an associated 2×2 matrix. Match the following linear transformations wi

zubka84 [21]

Answer:

1. Clockwise rotation by π/2 radians

: D

2. Reflection about the x-axis

: E

3. Counterclockwise rotation by π/2 radians

: F

4. The projection onto the x-axis given by T(x,y) = (x,0)

: C

5. Reflection about the y-axis : A

6. Reflection about the line y = x : B

Step-by-step explanation:

Given a linear transformation $T:\mathbb{R}^2\to\mathbb{R}^2$ , one matrix representation of T is obtained by stacking the vectors T(1,0) and T(0,1) in columns.

a) A counter clockwise rotation of $\pi/2$ radians sends (1,0) to (0,-1) and it sends (0,1) to (1,0), so the matrix representation is

$\left[\begin{matrix} 0& 1 \\ -1 & 0 \end{matrix}\right]$ which corresponds to matrix D.

From now on, I will provide the values of T(1,0) and T(0,1)

b) Reflection about the x-axis T(1,0) = (1,0) and T(0,1) = (0,-1), which corresponds to matrix E.

c) Counterclockwise rotation by π/2 radians T(1,0) = (0,1), T(0,1) = (-1,0). Matrix F

d) The projection onto the x-axis given by T(x,y) = (x,0). T(1,0) = (1,0) T(0,1) = (0,0). Matrix C

e) Reflection about the y-axis T(1,0) = (-1,0) T(0,1) = (0,1). Matrix A

f) Reflection about the line y = x. This transformation corresponds to interchanging the values of x and y. That is, send (x,y) to (y,x). So, in this case

T(1,0) = (0,1) T(0,1) = (1,0). Matrix B

7 0

4 years ago

If you flip three fair coins, what is the probability that you'll get at least two heads?

crimeas [40]

Answer:

the odds of it landing on heads two out of the 3 times is fair and ultimately and even 1/2 chance it will land on heads, as it has a 1/2 chance it will land on tails.

Hope this helps

4 0

4 years ago

Read 2 more answers

Identify the independent and dependent variables. The equation A=25w gives the area A (in square feet) of a rectangular dance fl

kozerog [31]

Answer:

The dependent variable is A

The independent variable is w

Step-by-step explanation:

Given

$A = 25w$

Required

Identify the variables

In $A = 25w$

The value of w is independent of the value of A.

In other words:

A derive its own value from w; by multiplying 25 and w.

Take for instance:

$w = 3$

The value of A would be:

$A = 25 * 3$

$A = 75$

Hence:

The dependent variable is A

The independent variable is w

7 0

3 years ago

Show that Circle R with center (2, -9) and radius 5 is similar to Circle Q with center (-4, 3) and radius 3 by using a series of

faltersainse [42]

Answer:

It can be proved that the circle R is similar to the circle Q by translating the circle R a displacement of (-6, 12).

Step-by-step explanation:

We can demonstrate that Circle R is similar to Circle Q by translating the center of the former one to the center of latter one. Meaning that every point of circle R experiments the same translation. Vectorially speaking, a translation is defined by:

$O'(x,y) = O(x,y) + T(x,y)$ (1)

Where:

$O(x,y)$ - Original point.

$O'(x,y)$ - Translated point.

$T(x,y)$ - Translation vector.

If we know that $O(x,y) = (2,-9)$ and $O'(x,y) = (-4,3)$ , then the translation vector is:

$T(x,y) = O'(x,y)-O(x,y)$

$T(x,y) = (-4,3) - (2,-9)$

$T(x,y) = (-6,12)$

It can be proved that the circle R is similar to the circle Q by translating the circle R a displacement of (-6, 12).

4 0

3 years ago

What is the slope of the line ?

Svetradugi [14.3K]

Slope of a line

m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}

m = slope

(x_1, y_1) = coordinates of first point in the line

(x_2, y_2) = coordinates of second point in the line

How do I find the slope of the line?

The slope equals the rise divided by the run: . You can determine the slope of a line from its graph by looking at the rise and run. One characteristic of a line is that its slope is constant all the way along it. So, you can choose any 2 points along the graph of the line to figure out the slope.

4 0

4 years ago

What is the answer to this? What are the 2 equations for this?