A rotation in the plane is determined by the angle of rotation (with respect to an established orientation).

A rotation has not eigenvectors.

A rotation preserves angles, distances and ortientation.

In the drawing we see what is the image a triangle by a rotation You can check how the rotation transforms the plane, modifying the angle and the vertices of the triangle. In particular, observe how the orientation of the angles of the initial triangle and of its image are not modified.