Question: In many situations it is desirable to consider two group elements the same if they differ by an element of a given subgroup. For example, in D4 above, once a reflection is performed, the square never gets back to the r2 configuration by just applying the rotation operations (and no further reflections), i.e. the rotation operations are irrelevant to the question whether a reflection has been performed. Cosets are used to formalize this insight: a subgroup H defines left and right cosets, which can be thought of as translations of H by arbitrary group elements g. In symbolic terms, the left and right cosets of H containing g are
Try to answer this question if possible: When is it preferable to consider two group elements to be the same?
Answer: irrelevant to the question whether a reflection has been performed
Question: In February 2015, YouTube announced the launch of a new app specifically for use by children visiting the site, called YouTube Kids. It allows parental controls and restrictions on who can upload content, and is available for both Android and iOS devices. Later on August 26, 2015, YouTube Gaming was launched, a platform for video gaming enthusiasts intended to compete with Twitch.tv. 2015 also saw the announcement of a premium YouTube service titled YouTube Red, which provides users with both ad-free content as well as the ability to download videos among other features.
Try to answer this question if possible: What happened in March 2015?
Answer: unanswerable
Question: Due to industrial restructuring and loss of jobs in the auto industry, Detroit lost considerable population from the late 20th century to present. Between 2000 and 2010 the city's population fell by 25 percent, changing its ranking from the nation's 10th-largest city to 18th. In 2010, the city had a population of 713,777, more than a 60 percent drop from a peak population of over 1.8 million at the 1950 census. This resulted from suburbanization, industrial restructuring, and the decline of Detroit's auto industry. Following the shift of population and jobs to its suburbs or other states or nations, the city has focused on becoming the metropolitan region's employment and economic center. Downtown Detroit has held an increased role as an entertainment destination in the 21st century, with the restoration of several historic theatres, several new sports stadiums, and a riverfront revitalization project. More recently, the population of Downtown Detroit, Midtown Detroit, and a handful of other neighborhoods has increased. Many other neighborhoods remain distressed, with extensive abandonment of properties.
Try to answer this question if possible: What industry has Detroit tried to revitalize in recent years?
Answer: entertainment
Question: The bacterial cell is surrounded by a cell membrane (also known as a lipid, cytoplasmic or plasma membrane). This membrane encloses the contents of the cell and acts as a barrier to hold nutrients, proteins and other essential components of the cytoplasm within the cell. As they are prokaryotes, bacteria do not usually have membrane-bound organelles in their cytoplasm, and thus contain few large intracellular structures. They lack a true nucleus, mitochondria, chloroplasts and the other organelles present in eukaryotic cells. Bacteria were once seen as simple bags of cytoplasm, but structures such as the prokaryotic cytoskeleton and the localization of proteins to specific locations within the cytoplasm that give bacteria some complexity have been discovered. These subcellular levels of organization have been called "bacterial hyperstructures".
Try to answer this question if possible: Absence of what make bacteria belong to prokaryotes?
Answer:
true nucleus, mitochondria, chloroplasts and the other organelles