Final answer:
Retroviruses use the enzyme reverse transcriptase to convert their RNA genomes into DNA within a host cell, producing a provirus that integrates with the host's DNA.
Step-by-step explanation:
The viruses capable of converting their RNA genomes into DNA are called retroviruses. They carry the enzyme reverse transcriptase, which synthesizes DNA from the viral RNA once inside a host cell. This newly synthesized DNA, called a provirus, integrates with the DNA of the host cell using the enzyme ligase, also provided by the virus. Consequently, the host cell then uses the viral DNA to produce more viral RNA and proteins for new virions.