With the part of the UV map selected that you want to rotate, hit <kbd>R</kbd> to enter rotation mode, then type the number of degrees with the numpad, for example <kbd>9</kbd><kbd>0</kbd> to rotate it 90°. Then hit <kbd>Enter</kbd> or <kbd>Return</kbd> to apply it, or just left click.

You can also scale the selection with <kbd>S</kbd> and then entering a numerical value, for example <kbd>2</kbd> to make it twice as large, or <kbd>.</kbd><kbd>5</kbd> to make it half the size.

You can also move the selection along the X or Y axis by hitting <kbd>G</kbd> to grab it, then constraining it to the X or Y axis with <kbd>X</kbd> or <kbd>Y</kbd>, then entering the number of units you want it to move.

This also works in the 3D viewport.