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Thus and origin
For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is
Thus, the total applied torque about the origin is given by
Thus, the sum of all applied forces and torques ( with respect to the origin of the coordinate system ) in the body can be given by
Thus, the word myth is of Greek origin, while pith is a Germanic word.
Thus, one cannot expect to find a clear origin.
Thus the total revenue curve for a monopoly is a parabola that begins at the origin and reaches a maximum value then continuously decreases until total revenue is again zero.
Thus the bound vector represented by ( 1, 0, 0 ) is a vector of unit length pointing from the origin along the positive x-axis.
Thus, it is not correct to establish a strict common origin, but a common cultural identity.
That word came from imbarrare, " to block " or " to bar ", which is a combination of in -, " in ", with barra, " bar " ( from the Vulgar Latin barra, which is of unknown origin ).< sup > 11 </ sup > The problem with this theory is that the first known usage of the word in Italian was by Bernardo Davanzati ( 1529 – 1606 ), long after the word had entered Spanish .< sup > 12 </ sup > Thus, modern scholars believe that the Italian word actually came from the Spanish one .< sup > 13 </ sup >
Thus the spelling of a word is dependent principally upon its structure, its relationship to other words, and its language or origin.
Thus the streamlines are circles that are tangent to the x-axis at the origin.
Thus, the major peculiarities of the ancient Greek political system were ; firstly, its fragmentary nature, and that this does not particularly seem to have tribal origin ; and secondly the particular focus on urban centres within otherwise tiny states.
Thus they express the intermediate filament protein vimentin, a feature used as a marker to distinguish their mesodermal origin.
Thus the word Guacara was pronounced Wakala by the Seminoles who are Muskhogean in their origin and language.
Thus Pennsylvania Dutch, the term, includes residents which historically lived near the " German " origin Pennsylvania Dutch of Germany, in both France and Switzerland, whose borders over time had been traded around to be included in one country and then another, and the Pennsylvania Dutch were not then technically JUST from Germany, although they did share common bloodlines and ancestries, living in close locale.
Thus, the origin and content of the concept of " electron " is questionable.
Thus the origin of the word ' Pohja ' in its use as " North ".
Thus the origin of terrestrial planets is now considered to be an almost solved problem.
Thus, he suggested that they are biological in origin and can therefore be safely and correctly categorised.
Thus the carpets produced became typical of the Indian origin and gradually the industry began to diversify and spread all over the subcontinent.
Thus the length of the spiral measured from the origin can be expressed as:
Thus, by 1928 basic physical understanding of the origin of CFE from bulk metals had been achieved, and the original Fowler-Nordheim-type equation had been derived.
Thus, a is a real Lorentz four-vector representing the change of space-time origin x ↦ x − a where x is in the Minkowski space M < sup > 4 </ sup > and L is a Lorentz transformation, which can be defined as a linear transformation of four-dimensional space-time which preserves the Lorentz distance c²t² − x ⋅ x of every vector ( ct, x ).

Thus and original
Thus, oxygen is reduced to water and the original electron acceptors NAD < sup >+</ sup > and quinone are regenerated.
Thus the Rump never had more than two hundred members ( less than half the number of the Commons in the original Long Parliament ).
Thus Jesus takes a firm stand on the permanence of marriage in the original will of God.
Thus, the sections of the original work numbered only to 102.
Thus their understanding of the Demiurge is similarly flawed in comparison to Plato ’ s original intentions.
Thus, the only practical use for the grasslands, which replaced the original bushland, was for dairy cattle.
Thus, Hannibal took the Romans by surprise a scant two years later in 218 BC by merely reviving and adapting the original Gaulish-Carthaginian invasion plan of his brother-in-law.
Thus, the original owner should not be entitled to S2, but rather, some or all of S3.
Thus the Ittō-ryū ( Single sword school ) indicates the founder's illumination that all possible cuts with the sword emanate from and are contained in one original essential cut.
Thus, the original definition was limited to structures of unicellular organisms.
Thus, Hannibal took the Romans by surprise a mere two years later ( 218 BC ) by merely reviving and adapting the original Gaulo-Carthaginian invasion plan of his brother-in-law Hasdrubal.
Thus, Adam's sin was " to set a bad example " for his progeny, but his actions did not have the other consequences imputed to original sin.
Thus, the final game was very stripped down from its original intentions, and instead featured gameplay similar to Doom and its sequel, although levels and enemies were closer to medieval RPG style rather than science-fiction.
Thus if a station was transmitting on 300 kHz and the oscillating receiver was set to 400 kHz, the station would be heard not only at the original 300 kHz, but also at 100 kHz and 700 kHz.
Thus the length of the edges is one third of that of the original edges.
Thus, the Republic of Ireland now has thirty-four ' county-level ' authorities, although the borders of the original twenty-six counties are still officially in place.
Thus, given the same mass as the original S-IVB, one can expect a moderate increase in overall performance using a nuclear engine.
Thus the original tunnels were moved to the side, as were several other bridges across the Chicago River-shown in detail on the city maps.
Thus, by the end of the 1st century AD Latin had finally displaced the original Venetic language.
Thus shales may pass into cordierite rocks, or may show large crystals of andalusite ( and chiastolite ), staurolite, garnet, kyanite and sillimanite, all derived from the aluminous content of the original shale.
Thus, sets of complementary wavelets are useful in wavelet based compression / decompression algorithms where it is desirable to recover the original information with minimal loss.
Thus, the original meaning of anomie defined anything or anyone against or outside the law, or a condition where the current laws were not applied resulting in a state of illegitimacy or lawlessness.
Thus, they are a more useful place to queue messages when the primary servers are offline than the original sender's queue.
Thus, the newly bred hybrid chestnut trees should reach the same heights as the original American chestnut.

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