the reason is that a year - the time it takes the earth to complete its journey around the sun - doesn't actually have a full number of days in it - in other words there is a small amount of extra time left over at the end of the year. So we add an extra day every 4 years to keep things synchronised. But, this still leaves a small error which calendar-makers correct for by skipping a leap-day 3 times every 400 years ! To work out which ones to leave out if the first 2 digits of the year are not divisible by 4 then they are skipped - so in the last 400 years, 1700, 1800, 1900 were NOT leap years (because 4 doesn't go into 17, 18 or 19), but 2000 was.

Yes, but with difficulty. The science behind it is that all objects have frequencies at which they naturally vibrate - you know that annoying rattle in your car that tends to be worst at certain speeds ? These frequencies are called resonant frequencies. When a singer makes a note sound waves travel through the air as a pressure wave which we hear because it makes our ear-drum vibrate in sympathy. In the same way a wine glass will vibrate. If you can hit the resonant frequency of the wine glass, by singing just the right note, and make the note loud enough, eventually the glass will try to vibrate more that the material is able to and it will shatter.

This is due to an effect called strobing. Although the computer screen looks like it is displaying a continuous picture, the image is actually being replaced with a fresh one between 65 and 100 times a second, so the screen behaves a bit like a large camera flash, taking 100 pictures per second. Since our eyes can only see things that are flashing at less than about 25 times per second, we see a continuous image on the screen. So what happens to your hand ? When you wave the screen is essentially taking a series of rapid snapshots of your hands, giving the bizarre impression that your fingers are jumping across the screen, and that you can see through them.