Somebody posed a question about starting and stopping the database from within the OEM tool as the SYSTEM rather than the SYS user. There’s actually a simple trick to do that, you connect to OEM as the SYSTEM user but when you startup or shutdown the database, you reconnect for those tasks as the SYS user.
I put together these screen shots from the point where the DBConsole and database are up and running. That means they show you how to shutdown the database before re-starting it.