I have no idea! Kind of...
If your RackSpace server functions essentially like a VPS or bare metal machine (just in the cloud), then you're all set! There are a couple way to go about it. I'll explain a couple of simple ways this works on a regular VPS or bare metal machine.
You have your web root and an EE installation working on it. One way to go is Multi Site Manager. This works well for multiple domains functioning from the same EE install. The instructions are relatively straight-forward.
If you want to keep these installations completely silo-ed, you can install a separate EE instance in a sub-folder of your web root:
Then you just need to set up your VirtualHost (for Apache) settings for that new folder to match your new second-site domain, set your DNS entries for the new domain to point at your RackSpace server, and make sure you set your new EE install to have the right server paths (
/my-web-root/second-ee-site/ instead of
/my-web-root/). I have a few EE sites that live in a sub-folder of my web-root, which is it's own EE site just like this.
If either of these methods applies to a RackSpace server... I don't know, since I don't have one. But again, if a RackSpace cloud server functions like a regular bare metal machine, just in the RackSpace cloud, you should be all set. I hope others chime in (or yourself) if I'm being particularly ignorant.
And oh, yes, you need a separate DB schema for each install. Well, you don't need, but trust me, you want.