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

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

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

This also works in the 3D viewport.

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

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

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

This also works in the 3D viewport. If you look at the bottom of the current viewport while doing a resize, scale, or movement operation, you can see the values you have entered in the bar beneath the viewport.