Monster

You pick up this monster hand:
K
AKQJxx
AQTx
Ax
You are in 4th position, vul vs not and while you are admiring your collection, LHO opens 4 Spades which is quickly passed to you. What do you bid?

Act or No?

I've been debating this hand and situation with a few friends--you hold, white v red at matchpoints:
QTxxx
x
Ax
KTxxx

The dealer opens 1 Heart on your left, partner passes and your RHO bids 4 Hearts. Do you bid? If so, what do you bid? What do you do at different vulnerabilities? Change the scoring to IMPs or rubber bridge and does your agenda differ? Similar situation--what if you held this hand and your RHO opened 4 Hearts in from of you? Tough problems, I doubt there is a clearcut right answer but I am interested in opinions!