Draw a segment from the origin, point O, to point R. Draw a segment from the origin, point O, to point R'. The angle of rotation is the angle between segments OR and OR'.
The slope of segment OR is 2/3.
The slope of segment OR' is -3/2.
The slopes are negative reciprocals, so the segments are perpendicular.
The angle between the segments is 90 degrees. The rotation is counterclockwise, so it is a negative number of degrees.
