A 2 times 2 orthogonal matrix

The matrix

 U = frac{1}{sqrt{2}} left(begin{array}{cc} 1 & 1  1 & -1 end{array}right)

is orthogonal.

The vector x = (2,1) is transformed by the orthogonal matrix above into

 Ux = frac{1}{sqrt{2}} left(begin{array}{c} 1  3 end{array}right).

Thus, U corresponds to a rotation of angle 45^o counter-clockwise.