Take a square and cut it as you wish into a finite number of pieces. Rearrange the pieces without rotating or flipping any of them to form an new square that is rotated 45-degrees compared to the
original.
As long as the square doesn't have to be the same size as the original square! Just cut off the corners, and you have a smaller, yet you have a "new square that is rotated 45-degrees compared to the original."
easy...
