I have no sweet clue what GNOME includes as a task manager, to be honest. Under KDE, there is a program called KSysGuard that works well, but as for a GNOME-equivalent, I have no idea. All of this information could be gathered through the command-line, though.
To see what application is using the most resources, just type
top. The applications in use will be sorted from top to bottom in terms of what's using the most resources. RES corresponds to how much physical RAM is used, while VIRT is how much RAM and SWAP is used, combined together.
To view all of the applications being used, you can use
ps. To view ALL applications that are in use, run
ps ax, which will show you a rather sizable list of what's being used right now. To see if a specific application is being used, such as Firefox, you can run a command like
ps ax | grep firefox which will filter out just Firefox and related components.
If you need to forcibly kill a task for some reason, note the PID to the left.
rwilliams@techgage ~ $ ps ax | grep amarokapp
4690 ? SLl 4:20 amarokapp
6282 ? S 1:08 amarokapp
11323 pts/2 S+ 0:00 grep --colour=auto amarokapp
In a case like that, I'd have to kill both 4690 and 6282 in order to fully terminate the application. The last one listed is just the command that was just run, and it ceases to exist after it's printed out. To kill an application like this, you'd run
kill -9 4690 6282 and say goodbye. Unlike Windows, killing an application like this under Linux actually works all of the time (unless it's somehow a zombie which happens very rarely).
If you don't mind dual booting that is. 
