Which countries on both sides of the atlantic experienced revolutions during the late 18th and early 19th centuries

in Portugal (1820) it was so-called "Liberal Revolution" (Revolucao Liberal), in Spain (1812 and then so-called "Liberal Three Years, 1820-1823),  in Argentina (1810) so-called "May Revolution" which led to proclamation of independence (1816), in Brazil (1822), in France (1789)

Explanation:

1. Portuguese royal family left Portugal for Brazil (1807) because of appoaching Napoleonian forces (general Junot). Then Portugal became British protectorate (lord Beresford). In 1820 Revolution took place not only to give constitution to the country and to limit absolute powers of king, but also to end British protectorate and bring heir apparent back (John VI). John VI got back and signed the constitution (1824).

2. in Spain 1812, first draft of constitution was made (city of Cadiz). It is where tradition of Spanish liberalism started. At that time Spain was occupied by Napoleonian France and defeated in 1813. In 1814 (Congress of Vienna) Bourbon dynasty was restored (Fernando VII). Liberals (constitutionalists) managed to impose constitution in 1820 but this period lasted only till 1823. Then absolutism was restored again.

3. In Argentina in 1810 "May Revolution" took place (inspired by ideals of French revolution) which led later to independence of Argentina (defeat of Spanish royalists) in 1816.

4. In Brazil, separation from Portugal was quite peaceful (1822) because took place within royal family. Royal heir apparent (Pedro, son of John VI) reject to return to Portugal which created quite a tension between Lisbon and Rio. Later on, he proclaimed independence (September, 7, 1822).

5. in France revolution took place in 1789. In fact it was a consequence of  irresponsible economics of French royal court (Bourbons). To impose higher taxes the king Louis XVI had to call for General States. But the authority of king, and all the monarchic state became quite fragile. Revolution started already  at General States when the Third State decided to form "National Assembly".

they made rome the dominant power in the mediterranean.

i would say your answer is a)

sorry if im wrong