Ok, It's the tank that needs to cycle, not the live rock. The live rock will
most likely have to be cured. This means that during shipment, the live rock has living things on it that will have died. It must be put in salt water, with circulation. The water needs to be checked, and changed, until the reoccurence of ammonia spikes caused by the die off stop.
A new tank must cycle. At initial set up. The cycle may be started by this live rock, or a dead shrimp. The water is checked daily. You will get an ammonia spike, then a nitrite spike(bacteria grows that changes ammonia), then nitrate(bacteria that changes nitrite).
Usuallly, this is when you do a water change. Check levels, if all the above stay at 0, then you are cycled.
Please, don't be offended if you know all this already, it just doesn't seem to me that a tank is cycled in 1 week. Hope this helps!