When the tcp\ip translates a network layer address into a data link layer address (after not finding an entry for the network layer address in its data link layer address table in the cache) , it sends a special to all computers in the subnet?

When the network stack translates an IP address (network address) to a MAC address (data link address) it sends a broadcast using ARP to all devices on the subnet asking who has the specified IP address.  The device with that IP address will then respond with it's MAC address to the ARP message's source.

With this in mind the answer to your question would either be broadcast or ARP request depending on what you have been learning in class.