Every rotation maps an orthonormal basis of R < sup > 3 </ sup > to another orthonormal basis.

Every proper rotation is the composition of two reflections, a special case of the Cartan – Dieudonné theorem.

Every nontrivial proper rotation in 3 dimensions fixes a unique 1-dimensional linear subspace of R < sup > 3 </ sup > which is called the axis of rotation ( this is Euler's rotation theorem ).

Every improper rotation of three-dimensional Euclidean space is rotation followed by a reflection in a plane through the origin.

Every rotation Rot ( φ ) has an inverse Rot (− φ ).

Every rotation in three dimensions is defined by its axis — a direction that is left fixed by the rotation — and its angle — the amount of rotation about that axis ( Euler rotation theorem ).

Previously a daily segment, Underbelly didn't appear as often in the rotation ( hence Maddow's inclination to add " Every day ... or so " to her introduction of the segment ).

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.

Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

Every single problem touched on thus far is related to good marketing planning.

Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.

Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.

Every man in every one of these houses is a Night Rider.

Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Every infinite game in which is a Borel subset of Baire space is determined.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.

Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

This was to be based on utilitarian principles ; he said: " Every man has a right to that, the exclusive possession of which being awarded to him, a greater sum of benefit or pleasure will result than could have arisen from its being otherwise appropriated.

Every karma produces a result which must be experienced either in this or some future life.

Every secondary color is the complement of one primary color ; when a primary and its complementary secondary color are added together, the result is white: cyan complements red, magenta complements green, and yellow complements blue.

Every vibrating object tends to maintain its plane of vibration if its support is rotated, a result of Newton's first law.

" In an interesting meditation on what he viewed as the harm which would result if Christian ideals were abandoned in Belgium, he said: " Every time society has distanced itself from the Gospel, which preached humility, fraternity, and peace, the people have been unhappy, because the pagan civilization of ancient Rome, which they wanted to replace it with, is based only on pride and the abuse of force " ( Commemorative speech for the war dead of the Battle of the Yser, given by Dom Marie-Albert, Abbot of Orval Abbey, Belgium, in 1936 ).

Every antiseptic, however good, is more or less toxic and irritating to a wounded surface ; as a result, in surgery, the antiseptic method has been replaced by aseptic method, which is preventative in nature and relies on keeping free from the invasion of bacteria rather than destroying them when present.

Nordau saw in Jewish Emancipation the result of ' a regular equation: Every man is born with certain rights ; the Jews are human beings, consequently the Jews are born to own the rights of man.

Every adverse effect is the result of a set of direct factors, the absence of any one of which would have resulted in the effect having been different than it was.

The Every One Campaign was started in October 2009 as a result of the Millennium Development Goals created in 2000.

Every Java 2D drawing operation can ultimately be treated as filling a shape using a paint and compositing the result onto the screen.

Every morning she picks him up from his flat in the patrol car and drops him off in the evening — provided the case they have been handling does not result in her ending up in hospital.

Every attack made will result in a character's bloodlust to rise.

* Maximillian, in which a young man who was paralysed in a car crash as a result of not wearing a seatbelt advises the audience to " Clunk Click Every Trip ".

Every international success was presented as a direct result of the righteousness of the communist rule and ideology.

Every step of the transportation chain will result in different stresses from shock and vibration.

Another " Viper Room " in Portland, Oregon, has also been told to stop using the name under threat of a trademark lawsuit, with owner Darin Feinstein claiming " Every dollar they make is the result of using our name.

Every time the sine wave's value hit " 3. 2 ," the truncated result would be off by 0. 2, as in the sample data above.

Every time the sine wave's value hit " 4. 0 ," there would be no error since the truncated result would be off by 0. 0, also shown above.

Every other time the value 4. 8 comes up the result is an error of 0. 2, and the other times it is – 0. 8.

* Every non-split, prime, alternating link that is not a torus link is hyperbolic by a result of William Menasco.

A British officer recorded the result in his diary: " Every horror was perpetrated with impunity – rape, murder, pillage – and not a single man was punished.

Every measurable entity maps into a cardinal function but not every cardinal function is the result of the mapping of a measurable entity.

Every operand byte or result byte required its own separate main memory cycle, which limited program performance.