Rotation question

[Steven G]

I was asked to answer this problem but am completely baffled by it. Hints or solution will be helpful.
The matrix
-5 +6
-6 -5
represents a rotation combined with a scaling.
What is the angle of rotation in degrees and the scale factor?

I know that the matrix that rotates a point in R^2 p degrees c-c-w is
+cos(p) -sin(p)
+sin(p) +cos(p)
and the given matrix is in that form. This is as far as I got.

 

[Cubist]

I know that the matrix that rotates a point in R^2 p degrees c-c-w is
+cos(p) -sin(p)
+sin(p) +cos(p)
and the given matrix is in that form. This is as far as I got.

Therefore a matrix that rotates and scales by "m" would be
+m*cos(p) -m*sin(p)
+m*sin(p) +m*cos(p)
...can you continue?

Spoiler: hint

use cos^2+sin^2 = 1 to help with finding m