Question

Find the transformation matrix that rotates a rectangular coordinate system through an angle of 120° (counterclockwise) about an axis making equal angles with the original three coordinate axes.

Answer 1

Since the coordinate system is rectangular, we have the matrix
[ x ]
[ y ]

The transformation matrix is
[ cos 120   sin 120 ] [ x ] = [ x' ]
[ -sin 120  cos 120 ] [ y ] = [ y' ]<span />