Problem: Group (mathematics):

Sub- and quotient groups are related in the following way: a subset H of G can be seen as an injective map H G, i.e. any element of the target has at most one element that maps to it. The counterpart to injective maps are surjective maps (every element of the target is mapped onto), such as the canonical map G G / N.y["] Interpreting subgroup and quotients in light of these homomorphisms emphasizes the structural concept inherent to these definitions alluded to in the introduction. In general, homomorphisms are neither injective nor surjective. Kernel and image of group homomorphisms and the first isomorphism theorem address this phenomenon.

What theory address the phenomenon of homomorphisms being neither injective nor surjective?
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A: the first isomorphism theorem

Problem: 2008 Sichuan earthquake:

In a United States Geological Survey (USGS) study, preliminary rupture models of the earthquake indicated displacement of up to 9 meters along a fault approximately 240 km long by 20 km deep. The earthquake generated deformations of the surface greater than 3 meters and increased the stress (and probability of occurrence of future events) at the northeastern and southwestern ends of the fault. On May 20, USGS seismologist Tom Parsons warned that there is "high risk" of a major M>7 aftershock over the next weeks or months.

How deep is the fault?
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A: 20 km deep

Problem: Armenia:

On 10 October 2009, Armenia and Turkey signed protocols on normalisation of relationships, which set a timetable for restoring diplomatic ties and reopening their joint border. The ratification of those had to be made in the national parliaments. In Armenia it passed through the required by legislation approval of the Constitutional Court and was sent to the parliament for the final ratification. The President had made multiple public announcements, both in Armenia and abroad, that as the leader of the political majority of Armenia he assured the ratification of the protocols if Turkey also ratified them. Despite this, the process stopped, as Turkey continuously added more preconditions to its ratification and also "delayed it beyond any reasonable time-period".

Who made it difficult to ratify the protocols to reopen the Armenian/Turkey border?
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A: Turkey

Problem: Cotton:

Cotton linters are fine, silky fibers which adhere to the seeds of the cotton plant after ginning. These curly fibers typically are less than 18 inch (3.2 mm) long. The term also may apply to the longer textile fiber staple lint as well as the shorter fuzzy fibers from some upland species. Linters are traditionally used in the manufacture of paper and as a raw material in the manufacture of cellulose. In the UK, linters are referred to as "cotton wool". This can also be a refined product (absorbent cotton in U.S. usage) which has medical, cosmetic and many other practical uses. The first medical use of cotton wool was by Sampson Gamgee at the Queen's Hospital (later the General Hospital) in Birmingham, England.

What part of wool is used for paper manufacture?
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A:
unanswerable