Yes, RPI provides mattresses when you live in a residence hall. I’m not sure that they’re new each year, but they’re in good condition. If you have an issue with it, you should be able to arrange getting a replacement with Residence Life. I would estimate that they are replaced every 2-4 years.
If you want, you could bring your own, but you would be responsible for storing the one that RPI provides. I suppose that if your parents will be driving you up to move you in, you could have them take the provided one home. I’ve never heard of someone using their own mattress though.
I would strongly advise that you get a mattress pad.