Final answer:
The memory responsible for holding the computer's date and time when powered off is a type of ROM, specifically the RTC, which is kept alive by a small battery called the CMOS battery.
Step-by-step explanation:
The memory used to store the computer's date and time while the computer is powered off is known as the Real-time Clock (RTC) memory, which is a type of Read-only Memory (ROM). Unlike RAM (Random Access Memory), which loses its data when the power is turned off, ROM is non-volatile and continues to store information without power. The RTC gets its power from a small battery on the motherboard, commonly known as the CMOS battery, which allows it to run even when the computer is shut down, to maintain system date and time.