Make a matrix A whose action is described as follows: The hit by A rotates everything Pi/4 counterclockwise radians, then stretches by a factor of 1.8 along the x-axis and a factor of 0.7 along the y-axis and then rotates the result by Pi/3 clockwise radians.

The required matrix is

Step-by-step explanation:

Matrix of rotation:

x' + iy' = (x + iy)(cosθ + isinθ)

x' = x cosθ - ysinθ

y' = x sinθ + ycosθ

In matrix form:

The matrix stretches by 1.8 on the x axis and 0.7 on the y axis

i.e. x' = 1.8x

y' = 0.7y

According to the question, the result is rotated by pi/3 clockwise radians

To get the matrix A, we would multiply matrices R, Q and P together.

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.

answer:   rotate 270° clockwise about (7, 1) and reflect across the line x = 7

step-by-step explanation:

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