Explain why the U. S. acquisitions of new territory grew so rapidly during this time period.

during this time the US acquired  Alaska, Hawaii, Puerto rico, Guam, and the Philippians. During this time the us was a rising military power, and many European countries no longer wanted their territory in the western hemisphere. The US was also growing as an economic superpower witch allowed them to purchase land from places like Russia.  

pepin the short[a] (german: pippin der kurze, french: pépin le bref, c. 714 – 24 september 768) was the king of the franks from 751 until his death. he was the first of the carolingians to become king.[b][2]

the younger son of the frankish prince charles martel and his wife rotrude, pepin's upbringing was distinguished by the ecclesiastical education he had received from the monks of st. denis. succeeding his father as the mayor of the palace in 741, pepin reigned over francia jointly with his elder brother carloman. pepin ruled in neustria, burgundy, and provence, while his brother carloman established himself in austrasia, alemannia and thuringia. the brothers were active in suppressing revolts led by the bavarians, aquitanians, saxons, and the alemanni in the early years of their reign. in 743, they ended the frankish interregnum by choosing childeric iii, who was to be the last merovingian monarch, as figurehead king of the franks.

b. major john c. frémont led a rebellion called the bear flag revolt.

explanation:

during the bear flag revolt, from june to july 1846, a small group of american settlers in california rebelled against the mexican government and proclaimed california an independent republic. the republic was short-lived because soon after the bear flag was raised, the u.s. military began occupying california, which went on to join the union in 1850. the bear flag became the official state flag in 1911.