I wonder if we close the application. Does it completely close or it still run? I heard some one mention that when we close the application it still run for about 30 mins before completely close. So assume it is the case that these application still running, how can we know it and how to shut it completely?. In addition, dose it harm the ipad battery if it not completely shut.

When you say 'close the application' it depends exactly what you mean by that. If you simply mean 'switch to another application' - say moving from iPod to Pages then, no, the application - or at least some of its functionality - is still active.

If you mean, double-click the Home button to open the multi-task bar, then press and hold any icon until they jiggle, then press the '-' on the upper left-hand corner to close the application, then - no - no activity is left operational, as far as I'm aware.... and I've just checked and - for the apps I looked at (iPod) - I am right

Tim