Precalculus Matrices Transformations Problem

Question

A transformation rotates about the origin by an angle of  counter-clockwise, then dilates (with center at the origin) by a factor of  Find the matrix for this transformation.

Any help would be appreciated :)

Answer 1

You can use the general rotation (for angle θ: | cosθ sinθ| and put in the sin45 and cos45 = sqrt(2)/2)

| -sinθ cosθ|

You can make the rotation dilate by multiplying each term by the dilation factor sqrt(2) which leads to a matrix of ones (+/- 1)