7)  Explain how to determine how long Mars takes to rotate once
    about its axis.  Why does the method not work for Venus?

This is done by watching some feature on the surface of Mars, and simply timing how long it takes from the time that feature rotates to the edge of the planet's disk, as we see it from Earth, until the next time it rotates to the edge of the disk. This doesn't work for Venus because it is completely covered in clouds. You can't see any features on the surface (and the clouds are moving relative to the surface, so it won't help to watch a feature on the clouds).