Give two types of management of either hardware or other resources that are performed by an operating system.

Memory Management, Processor Scheduling.
Memory management allocates a specific area of memory to each application or open file while the computer is running. If the computer's RAM is not enough for a particular program, virtual memory may be used - contents that would be placed in RAM are copied to the hard drive while you are not using the program. When you switch back to the application, the contents are copied back to memory.
Processor Scheduling is how a computer is able to run multiple applications simultaneously. The OS allocates processor time fairly to each process (application) as they compete for the CPU. The scheduler has the main objectives of maximising throughput, being fair to all users, and provide acceptable response times.