To what was french historian alexis de tocqueville referring to when he wrote that americans did not believe "that democratic principles should undermine the husband's authority and make it doubtful who is in charge of the family"?

He referred to the fact that gender equality was not part of the democratic principles in which the American system of government was based.

Explanation:

The initial years of the US state were not revolutionary in the view of the family as the base of society. Furthermore, religious sentiment was part of the American lifestyle, a Christian view of the family. As such, for the Americans in the first phase of the US democracy, women were not subject to political rights and were expected to be supportive of men.

the expansion of the rule of empires over other territories took place as a result of several reasons including economic, ethnocentric, political, and religious, and exploratory purposes.

in terms of economic purposes: imperial governments aimed to maximize profits and with that purpose they neeeded cheap labor, access to or control of markets to sell or buy products. they also desired to find natural resources (precious metals and land). in the awake of   industrial revolution, dependent colonies provided the necessary raw materials that european factories and market needed to manufacture products.  

ethnocentric: many territories were conquered by imperial territories in an attempt to spread their cultures, values and belief as they considered them to be superior. in the late 19th century, for example, european powers held   the racist belief that inferior races should be conquered in order to “civilize” them.

political: another reason that drove conquer and expansion was patriotism and growing imperial power. it refers to national prestige, pride, and security. empires sought strategic territory to ensure access for their navies and armies around the world.

religious: the aim of converting new member of other religions was another factor that prompted expansion.   christian missionaries from europe established churches in conquered territories during the nineteenth century. thus, they spread western cultural values. furthermore, the imperial nation’s language was spread as well, through educational and religious interactions.

exploratory: imperial nations or their citizens aimed to explore territory that was unknown to them,   for different purposes including medical or scientific research, however, at the very   beginning, they did it to embark on adventure. furthermore, imperial explorers sought to discover, map, and claim territory before their imperial competition did, for national and personal glory as well as to realize the imperialist goal of expansion.

c) troops march forward in close formation against newer, more accurate weapons