Rotations

Very few rotations will take the strip to itself.

Centers:

Where can the center of rotation be if the rotation takes the strip to itself? If the center is not in the middle of the strip, think about a circle through that center just touching one edge of the strip but not the other. What happens under the rotation to points near that circle?

Angles:

Suppose the center of rotation is on the midline y=0. What angles of rotation are possible if all points of the strip are to go to points on the strip? Think about points near a circle just touching both edges of the strip.