Flashing an official Samsung galaxy tab kernel
First off you will need to root your tablet. This is relatively easy, especially with the galaxy because it's so popular. Head on over to the XDA Forums (www.xda-developers.com) and navigate to the galaxy 10.1 section. This youtube video also will do it for you: http://www.youtube.com/watch?v=krQDP7xYlWg

BE CAREFUL. Follow the steps exactly. You don't want to brick your device.

After that, you'll have ClockworkMod. So first things first: zip up your kernel, then copy it to your device. Most of the time, tablets require sd-cards in order to install things from recovery, so pop in an sd-card and copy the zipped folder here.

Then, reboot into recovery (turn device off, then hold up volume button and power at the same time). You'll want to wipe your cache partition and davlik cache first. Once this is done, go to install zip from sd-card, find your folder with the kernel, and that's it!

BEFORE YOU DO THIS, do a backup of your current system, just in case your kernel really messes up your device. Hope this helps!