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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 ).
Some Related Sentences
Every and nontrivial
Every formally real Jordan algebra can be written as a direct sum of so-called simple ones, which are not themselves direct sums in a nontrivial way.
Every and proper
Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.
* Every continuous map from a compact space to a Hausdorff space is closed and proper ( i. e., the pre-image of a compact set is compact.
* In any ring R, a maximal ideal is an ideal M that is maximal in the set of all proper ideals of R, i. e. M is contained in exactly 2 ideals of R, namely M itself and the entire ring R. Every maximal ideal is in fact prime.
Every year, thousands of cases of plague are still reported to the World Health Organization, although, with proper treatment, the prognosis for victims is now much better.
Every proper rotation is the composition of two reflections, a special case of the Cartan – Dieudonné theorem.
Every element in O ( 1, 3 ) can be written as the semidirect product of a proper, orthochronous transformation and an element of the discrete group
# Every man shall be called fairly in turn by the list on board of prizes, because over and above their proper share, they are allowed a shift of clothes.
Every Riemann surface is the quotient of a free, proper and holomorphic action of a discrete group on its universal covering and this universal covering is holomorphically isomorphic ( one also says: " conformally equivalent ") to one of the following:
Every elder in the Church is or should be an apostle ; that is, as a minister of the Lord and as a recipient of personal revelation from the Holy Ghost, every elder has the call to bear witness of the truth on all proper occasions.
: Every vessel must at all times maintain a proper look-out by sight ( day shape or lights by eyes or visual aids ) and hearing ( sound signal or Marine VHF radio ) as well as by all available means ( e. g., Radar, Automatic Radar Plotting Aid ( ARPA ), Automatic Identification System ( AIS ), GMDSS ...) in order to make a full assessment of the situation and risk of collision.
Every proper coloring and cocoloring of a graph are also subcolorings, so the subchromatic number of any graph is at most equal to the cochromatic number, which is at most equal to the chromatic number.
Every infinitesimal region of space time may have its own proper time that corresponds to the gravitational time dilation there, where electromagnetic radiation and matter may be equally affected, since they are made of the same essence ( as shown in many tests involving the famous equation E = mc < sup > 2 </ sup >).
Every proper subgroup of G can be assumed a solvable group, meaning that much theory of such subgroups could be applied.
* The embedding theorem for Stein manifolds states the following: Every Stein manifold of complex dimension can be embedded into by a biholomorphic proper map.
He summed up his philosophy by saying: " Every Plant has fitness and must be placed in its proper surroundings so as to bring out its full beauty.
Every living thing was related in a branching pedigree, not ascending a Lamarckian ladder, and this pedigree was the proper basis for classification.
Every ornament is at a proper distance, and not one too large, but all delicate and new, with more freedom and variety than Greek ornaments ; and, though probably borrowed from the Hotel de Condé and other new Palaces, not one that is not rather classic than French.
: Every person who under color of any statute, ordinance, regulation, custom, or usage, of any State or Territory or the District of Columbia, subjects, or causes to be subjected, any citizen of the United States or other person within the jurisdiction thereof to the deprivation of any rights, privileges, or immunities secured by the Constitution and laws, shall be liable to the party injured in an action at law, Suit in equity, or other proper proceeding for redress, except that in any action brought against a judicial officer for an act or omission taken in such officer's judicial capacity, injunctive relief shall not be granted unless a declaratory decree was violated or declaratory relief was unavailable.
Every barangay has a Catholic Chapel, which are maintained by the Lay Ministers Of St. Bartholomew Parish Church-Located in the town proper of San Manuel.
Every barangay ( village ) has its own Roman Catholic chapel aside from the parish church in the town proper.
Every psyker is in danger of going insane or being possessed by a daemon if he does not have the proper training and strength of will.
Every and rotation
Every rotation is the result of reflecting in an even number of reflections in hyperplanes through the origin, and every improper rotation is the result of reflecting in an odd number.
Every improper rotation of three-dimensional Euclidean space is rotation followed by a reflection in a plane through the origin.
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 and 3
Every tile belongs to the two suits of its two values, e. g. 0 – 3 belongs both to the blank suit ( or 0 suit ) and to the 3 suit.
Every IKEA store, including those run by Ingka Holding, pays a franchise fee of 3 % of the revenue to Inter IKEA Systems.
Every twin prime pair except ( 3, 5 ) is of the form ( 6n − 1, 6n + 1 ) for some natural number n, and with the exception of < var > n </ var > = 1, < var > n </ var > must end in 0, 2, 3, 5, 7, or 8.
Every third odd number is divisible by 3, which requires that no three successive odd numbers can be prime unless one of them is 3.
They draw three conclusions from Austin: ( 1 ) A performative utterance does not communicate information about an act second-hand — it is the act ; ( 2 ) Every aspect of language (" semantics, syntactics, or even phonematics ") functionally interacts with pragmatics ; ( 3 ) There is no distinction between language and speech.
Every sedenion is a real linear combination of the unit sedenions 1, < var > e </ var >< sub > 1 </ sub >, < var > e </ var >< sub > 2 </ sub >, < var > e </ var >< sub > 3 </ sub >, ..., and < var > e </ var >< sub > 15 </ sub >,
Every autumn, according to Plutarch ( Life of Lycurgus, 28, 3 – 7 ), the Spartan ephors would pro forma declare war on the helot population so that any Spartan citizen could kill a helot without fear of blood or guilt ( crypteia ).
* Every rule of thumb on earth in one place-A user participation reference project based on Tom Parker's 3 best-selling books and more than 25 years of research.
Every year, a small number of graduates do this-usually 3 or 4, and usually in a one-for-one " trade " with a similarly inclined cadet at one of the other service academies.
Every weekday, more than 1. 3 million people commute to the Argentine capital for work and other business.
Every year, the parade steps off from St Joseph the Worker Church, and proceeds two miles ( 3 km ) on New Falls Road to Conwell-Egan Catholic High School.
Every May since 1993, thousands of cagers have descended upon Thermopolis for the annual 3 on 3 Hot Spot Shootout Basketball Tournament.
Every mRNA consists of three parts-5 ' untranslated region ( 5 ' UTR ), protein-coding region or open reading frame ( ORF ) and 3 ' untranslated region ( 3 ' UTR ).