It doesn't depend on the height.
Now you are on the rotating Earth, so you rotate with it (around the axe of Earth's rotation). Its speed is between 0 (on the poles) and around 1.5 Mach on the Equator (1 Mach = the sound of speed).
If you want to compensate this rotation, there are many ways, for example, you can simply sit on an airplane capable to go with this speed, and flying in the opposite direction. Concordes could to that, current passanger airplanes can do this only from around $55^\circ$ of the Equator. On them, the Sun went into the opposite direction on the Sky and you arrived earlier (in the local time) as you started the voyage. They flight faster as the Earth rotated below them.
But the ISS does not this. The ISS is on orbit, with around 25 Mach. Actually, it is going much faster as it would be needed to compensate the Earth's rotation. And it is going into around the same direction as the Earth rotates (not perfectly, there is around a $30^\circ$ angle between its orbit and the equator). It is done so, because this speed is needed to compensate the Earth's gravity by centrifugal force. If it would be slower (it had been much cheaper), it would fall.