How many times do the hour hand and minute hand of a clock coincide with each other in a single day (24 hours)?

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?