Problem:The name "dot product" is derived from the centered dot ``" that is often used to designate this operation; the alternative name "scalar product" emphasizes that the result is a scalar, rather than a vector, as is the case for the vector product in three-dimensional space.

Based on this passage, the dot product of two vectors results in a?
Solution:OK... To answer this question, we should know that: " that is often used to designate this operation; the alternative name "scalar product" emphasizes that the result is a scalar, rather than a vector, as is the case for the vector product in three-dimensional space.
a scalar.


Student A:The three major constituents of air, and therefore of Earth's atmosphere, are nitrogen, oxygen, and argon. Water vapor accounts for roughly 0.25 % of the atmosphere by mass. The concentration of water vapor (a greenhouse gas) varies significantly from around 10 ppm by volume in the coldest portions of the atmosphere to as much as 5 % by volume in hot, humid air masses, and concentrations of other atmospheric gases are typically quoted in terms of dry air (without water vapor). The remaining gases are often referred to as trace gases, among which are the greenhouse gases, principally carbon dioxide, methane, nitrous oxide, and ozone. Filtered air includes trace amounts of many other chemical compounds. Many substances of natural origin may be present in locally and seasonally variable small amounts as aerosols in an unfiltered air sample, including dust of mineral and organic composition, pollen and spores, sea spray, and volcanic ash. Various industrial pollutants also may be present as gases or aerosols, such as chlorine (elemental or in compounds), fluorine compounds and elemental mercury vapor. Sulfur compounds such as hydrogen sulfide and sulfur dioxide (SO) may be derived from natural sources or from industrial air pollution.

Answer this question based on the passage: what are the main components of earth's atmosphere?
Student B:OK... This is the relevant information: The three major constituents of air, and therefore of Earth's atmosphere, are nitrogen, oxygen, and argon.
nitrogen , oxygen , and argon.


Problem:He returned to Young & Rubicam, hired by Chairman and CEO Alex Kroll, to work at their direct marketing division Wunderman. At Y&R companies, Becker created the award winning 25-year television campaign, "I'm stuck on Band-Aid' cause Band-Aid's stuck on me". ("Mike Becker and I wrote the song. Barry Manilow got the residuals. John Travolta and Terri Garr both launched careers," states Harry Webber, Becker's collaborator on this project, which led to a 1976 Clio Award and the composition of one of the most recognizable advertising jingles of all time.) He led the creation and production of the 10-year American Express Corporate Card campaign "To Your Success".

Who wrote the jingle im stuck on band aid?
Solution:OK... To answer the question, consider the following: At Y&R companies, Becker created the award winning 25-year television campaign, "I'm stuck on Band-Aid' cause Band-Aid's stuck on me".
Mike Becker.


Student A:Context: Annie Get Your Gun is a musical with lyrics and music by Irving Berlin and a book by Dorothy Fields and her brother Herbert Fields. The story is a fictionalized version of the life of Annie Oakley (1860 -- 1926), a sharpshooter who starred in Buffalo Bill's Wild West, and her romance with sharpshooter Frank E. Butler (1847 -- 1926).

Question: who wrote the music for annie get your gun?
Student B:OK... To answer this question, we should know that: Annie Get Your Gun is a musical with lyrics and music by Irving Berlin and a book by Dorothy Fields and her brother Herbert Fields.
Irving Berlin.


Problem:Passage: "All work and no play makes Jack a dull boy" is a proverb. It means that without time off from work, a person becomes both bored and boring. The exact origins of the phrase remain unclear, though it was recorded as early as 1659.

Question: Based on this passage, where does all work and no play makes jack a dull boy come from?
Solution:OK... This is the relevant information: The exact origins of the phrase remain unclear, though it was recorded as early as 1659.
unclear , though it was recorded as early as 1659.


Problem:Passage: The design process was initiated when, in 1999, the Department of Arts, Culture, Science and Technology requested ideas for the new coat-of-arms from the public. A brief was then prepared based on the ideas received, along with input from the Cabinet. The Government Communication and Information System then approached Design South Africa to brief ten of the top designers. Three designers were chosen to present their concepts to the Cabinet. Iaan Bekker's design was chosen.

Question: Based on this passage, who designed the national coat of arms of south africa?
Solution:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
OK... This is the relevant information: Iaan Bekker's design was chosen.
Iaan Bekker.