Do they replace your macs for you?

My macbook is screwy and the battery can't go 5 minutes without being plugged in otherwise it shuts down and when i go to sites or if i try to write an email the internet closes and it does that with iPhoto and iMovie and stuff like that. iTunes doesn't work on my computer either. I think this mac is 2 years old and it's under a warranty. It is my older brother's old one. He got a new one. I am going to take it to the apple store so do you think they will replace it since it's under warranty? I would love it if they do.