When a new family takes control, then a new dynasty begins. The Mandate of Heaven is what the Chinese people believed gave their rulers the right to be king or emperor. It meant that the gods had blessed that person with the right to rule. A ruler had to be a good and just ruler to keep the Mandate of Heaven.
A - Although he denies them, Dr. Vasequez faced several scandals last year.
A complex sentences must have both a dependent clasuse (although he denies them) and an independent clause (Dr. Vasquez faced several scandals last year.
Options B and D are compound sentences (two independent clauses) and option C is a simple sentence.