I understand that these pickups are like a fatter and warmer single-coil, or a smoother humbucker... I just can't really get a sound in my head to think of this. Are there any examples where that kind of tone can be clearly heard? Or, on which songs live can I hear Matt using his? Are they good for heavy rockin out?

Funkyriffic

Click for the greatest coincedence in the history of MuseLive!
http://www.muselive.com/forums.php?m=posts&p=1485398#1485398

Why did the tiger get lost? - Because the jungle is massive.

I think he uses it during Time is Running Out in the most recent gigs. I kinda realized this when I was using a P-90 and playing along to the song.

hmmm after trying to track down a video I think another example that gives a good sense of a P-90 tone is the improv track on HAARP (played before TIRO).

http://www.youtube.com/watch?v=MCwRGg4aJdo

I'm not that well-versed in guitar tone so maybe others can help you better haha

Warfield, San Francisco 9/21/04
Bill Graham Civic (NSSN), San Francisco 12/10/04
Concourse, San Francisco 7/18/06
Wembley, London 6/17/07
Verizon Wireless Amphitheatre, Irvine 9/21/07
Oracle Arena, Oakland 4/14/10
Arco Arena, Sacramento 9/28/10

On a side note - that improv is awesome, as is the tone he gets

Matt has P-90s in his Kaoss, Mirror (possibly the Seattle as well), and in the new one with the locking trem (I think it's called either Ali top or New Delorean). If you watch live performances, you'll catch P-90 in Starlight, Invincible, Time is Running Out (since 2006), Assassin, Plug in Baby (again, since 2006), Knights of Cydonia (occasionally), Hysteria (occasionally), and Dead Star (since 2008, and only if his guitar is black). P-90s are very versatile, and if wound correctly, can be used for damn near anything. I just got a Mississippi Queen for the bridge of my strat and I just might be off of humbuckers for good...

Bare Knuckle changed my life.