How many times in a single day (24 hours) are the two hands of a clock at right angles (90°) to each other?

What is the angle between the hour hand and the minute hand of a clock at 12:55?

There are two clocks, both set to show 10 p.m. on 21st January, 2010. One clock gains 2 minutes in an hour and the other clock loses 5 minutes in an hour. By how many minutes do the two clocks differ at 4 p.m. on 22nd January, 2010?