Questions about Orthogonal Transformations 1 how to prove a 2×2 matrix is a rotation matrix and find the angle of rotation.

Questions about Orthogonal Transformations

1

how to prove a 2×2 matrix is a rotation matrix and find the angle of rotation.

just show me an example

2

Q=1/9 * 4 -7 -4

1 -4 -8

8 4 1

 how to find the axis of rotation, the plane of reflection and the cosine of the angle of rotation?