Problem: In the example above, the identity and the rotations constitute a subgroup R = {id, r1, r2, r3}, highlighted in red in the group table above: any two rotations composed are still a rotation, and a rotation can be undone by (i.e. is inverse to) the complementary rotations 270° for 90°, 180° for 180°, and 90° for 270° (note that rotation in the opposite direction is not defined). The subgroup test is a necessary and sufficient condition for a subset H of a group G to be a subgroup: it is sufficient to check that g−1h ∈ H for all elements g, h ∈ H. Knowing the subgroups is important in understanding the group as a whole.d[›]
What rotation can a rotation be reversed by?
The answer is the following: inverse

Problem: The migration-period peoples who later coalesced into a "German" ethnicity were the Germanic tribes of the Saxons, Franci, Thuringii, Alamanni and Bavarii. These five tribes, sometimes with inclusion of the Frisians, are considered as the major groups to take part in the formation of the Germans. The varieties of the German language are still divided up into these groups. Linguists distinguish low Saxon, Franconian, Bavarian, Thuringian and Alemannic varieties in modern German. By the 9th century, the large tribes which lived on the territory of modern Germany had been united under the rule of the Frankish king Charlemagne, known in German as Karl der Große. Much of what is now Eastern Germany became Slavonic-speaking (Sorbs and Veleti), after these areas were vacated by Germanic tribes (Vandals, Lombards, Burgundians and Suebi amongst others) which had migrated into the former areas of the Roman Empire.
What king united the tribes in the 9th century? 
The answer is the following: Charlemagne

Problem: During the later Roman Empire, the principal military developments were attempts to create an effective cavalry force as well as the continued development of highly specialised types of troops. The creation of heavily armoured cataphract-type soldiers as cavalry was an important feature of the 5th-century Roman military. The various invading tribes had differing emphasis on types of soldiers—ranging from the primarily infantry Anglo-Saxon invaders of Britain to the Vandals and Visigoths, who had a high proportion of cavalry in their armies. During the early invasion period, the stirrup had not been introduced into warfare, which limited the usefulness of cavalry as shock troops because it was not possible to put the full force of the horse and rider behind blows struck by the rider. The greatest change in military affairs during the invasion period was the adoption of the Hunnic composite bow in place of the earlier, and weaker, Scythian composite bow. Another development was the increasing use of longswords and the progressive replacement of scale armour by mail armour and lamellar armour.
What Scythian weapon was used during this era?
The answer is the following: composite bow

Problem: Early civilisations in Myanmar included the Tibeto-Burman-speaking Pyu city-states in Upper Burma and the Mon kingdoms in Lower Burma. In the 9th century, the Bamar people entered the upper Irrawaddy valley and, following the establishment of the Pagan Kingdom in the 1050s, the Burmese language, culture and Theravada Buddhism slowly became dominant in the country. The Pagan Kingdom fell due to the Mongol invasions and several warring states emerged. In the 16th century, reunified by the Taungoo Dynasty, the country was for a brief period the largest empire in the history of Southeast Asia. The early 19th century Konbaung Dynasty ruled over an area that included modern Myanmar and briefly controlled Manipur and Assam as well. The British conquered Myanmar after three Anglo-Burmese Wars in the 19th century and the country became a British colony. Myanmar became an independent nation in 1948, initially as a democratic nation and then, following a coup d'état in 1962, a military dictatorship.
When did the dominant religion of Myanmar become something outside of the mainstream ? 
The answer is the following:
in the 1050s, the Burmese language, culture and Theravada Buddhism slowly became dominant in the country.