Problem: Exchanging "+" and "−" in the expression, i.e. permuting the two solutions of the equation can be viewed as a (very simple) group operation. Similar formulae are known for cubic and quartic equations, but do not exist in general for degree 5 and higher. Abstract properties of Galois groups associated with polynomials (in particular their solvability) give a criterion for polynomials that have all their solutions expressible by radicals, i.e. solutions expressible using solely addition, multiplication, and roots similar to the formula above.
Which group cannot be expressed using radicals?
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Answer: unanswerable


Problem: The Nazi regime under Adolf Hitler came to power in 1933, and along with Mussolini's Italy sought to gain control of the continent by the Second World War. Following the Allied victory in the Second World War, Europe was divided by the Iron Curtain. The countries in Southeastern Europe were dominated by the Soviet Union and became communist states. The major non-communist Southern European countries joined a US-led military alliance (NATO) and formed the European Economic Community amongst themselves. The countries in the Soviet sphere of influence joined the military alliance known as the Warsaw Pact and the economic bloc called Comecon. Yugoslavia was neutal.
Which group took control in 1933?
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Answer: The Nazi regime


Problem: The above explanation is merely a simple introduction to vacuum pumping, and is not representative of the entire range of pumps in use. Many variations of the positive displacement pump have been developed, and many other pump designs rely on fundamentally different principles. Momentum transfer pumps, which bear some similarities to dynamic pumps used at higher pressures, can achieve much higher quality vacuums than positive displacement pumps. Entrapment pumps can capture gases in a solid or absorbed state, often with no moving parts, no seals and no vibration. None of these pumps are universal; each type has important performance limitations. They all share a difficulty in pumping low molecular weight gases, especially hydrogen, helium, and neon.
Dynamic pumps often work without moving parts, seals and what?
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Answer:
unanswerable