My new cat is mean...any suggestions?

I currently have a 1 yr old neutered male. I recently got a new cat, female, spayed, and 4 yrs old. Ive had them separated but she is super mean to me. One minute she purrs a lot and the next she swats me and theres bloodshed. My current cat is being an absolute sweetheart. He rolls over alot in front of her and just walks up to her slowy and backs away when she hisses. I couldnt have asked for anything more than the dominant resident cat to act so tamed and calm about a new cat. But the new cat is just seemingly very aggressive. Im not sure if it is because she is petrified but that is what I tell myself so that I can still hope that she will adjust. Its only been 2 days but I havent witnessed such anger and fear in a cat and I just feel bad for her. Any suggestions?