id hand a copy of it to your boss and let him know you send it to HR. Just so everyone knows. Its not like its secret information.

Professional courtesy is 2 weeks, and the NEW JOB should understand the 2 week notice, most places understand that.

However, if this is a low wage labor job (NOT BEING FACETIOUS) just saying if its a 7-12$/hr job, 2 weeks really doesnt matter. They dont need 2 weeks notice and most places like that would rather you just left so they can hire a replacement