Question

a square rotated about its center by 360° maps on to itself at (1, 2, 3, or 4) different angles of rotation.

Answer 1

Answer: no rotation because only reflections through the center of a square can map it onto itself

Answer 2

A square rotated around its center maps onto itself every 90° of rotation.
If you rotate it a full 360°, then that happens 4 times.