Problem: Saint Helena was first settled by the English in 1659, and the island has a population of about 4,250 inhabitants, mainly descended from people from Britain settlers ("planters") and soldiers and slaves who were brought there from the beginning of settlement initially from Africa (the Cape Verde Islands, Gold Coast and west coast of Africa are mentioned in early records), then India and Madagascar. Eventually the planters felt there were too many slaves and no more were imported after 1792.
When was Saint Helena first settled?
The answer is the following: 1659

Problem: Due to reciprocity (discussed above) the gain of an antenna used for transmitting must be proportional to its effective area when used for receiving. Consider an antenna with no loss, that is, one whose electrical efficiency is 100%. It can be shown that its effective area averaged over all directions must be equal to 2/4, the wavelength squared divided by 4. Gain is defined such that the average gain over all directions for an antenna with 100% electrical efficiency is equal to 1. Therefore, the effective area Aeff in terms of the gain G in a given direction is given by:
hat could an antenna with complete electrical efficiency be said to have?
The answer is the following: 1

Problem: The Supreme Court ruled in the Head Money Cases that "treaties" do not have a privileged position over Acts of Congress and can be repealed or modified (for the purposes of U.S. law) by any subsequent Act of Congress, just like with any other regular law. The Supreme Court also ruled in Reid v. Covert that any treaty provision that conflicts with the Constitution are null and void under U.S. law.
In what cases did the US Supreme Court rule that treaties do not have a privileged position over Acts of Congress?
The answer is the following: Head Money Cases

Problem: The 9th- and 10th-century mosaics of the Hagia Sophia in Constantinople are truly classical Byzantine artworks. The north and south tympana beneath the dome was decorated with figures of prophets, saints and patriarchs. Above the principal door from the narthex we can see an Emperor kneeling before Christ (late 9th or early 10th century). Above the door from the southwest vestibule to the narthex another mosaic shows the Theotokos with Justinian and Constantine. Justinian I is offering the model of the church to Mary while Constantine is holding a model of the city in his hand. Both emperors are beardless this is an example for conscious archaization as contemporary Byzantine rulers were bearded. A mosaic panel on the gallery shows Christ with Constantine Monomachos and Empress Zoe (10421055). The emperor gives a bulging money sack to Christ as a donation for the church.
When did the Empress Zoe die?
The answer is the following:
1055