I was reading the untap step rule and got confused a bit. It says:
502.2. Second, the active player determines which permanents he or she controls will untap. Then he or she untaps them all simultaneously. This turn-based action doesn't use the stack. Normally, all of a player's permanents untap, but effects can keep one or more of a player's permanents from untapping.
If "a player determines", can I determine not to untap all my permanents?