For counterclockwise rotation:
┌ ┐
│ cos (theta) sin (theta) 0 │
[ x' y' 1 ] = [ x y 1 ] * │ -sin (theta) cos (theta) 0 │
│ 0 0 1 │
└ ┘
For clockwise rotation:
┌ ┐
│ cos (theta) -sin (theta) 0 │
[ x' y' 1 ] = [ x y 1 ] * │ sin (theta) cos (theta) 0 │
│ 0 0 1 │
└ ┘