Thus a disc rotating at 60 revolutions per minute ( rpm ) is said to be rotating at either 2π rad / s or 1 Hz, where the former measures the angular velocity and latter reflects the number of complete revolutions per second.

Thus, to convert from radians to degrees, multiply by 180 / π.

Thus, when analyzing earthbound motions, the Earth frame is not an inertial frame, but rather rotates about the local vertical at an effective rate of radians per day.

Thus, perpendicular components of forces acting on massless particles simply change their direction of motion, the angle change in radians being GM / rc < sup > 2 </ sup > with gravitational lensing, a result predicted by general relativity.

Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

Thus jazz is transmuted into something holy, the sacred road to integration of being.

Thus the fictional detective is much more than a simple businessman.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus in both types attention is focused on the community itself, and its phenomenological life.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

Thus human perception and human volition is the immanent cause of all social change and this most truly when the change reaches the civilizational level.

Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.

Thus the copywriter in the world of the space merchants is the person who in earlier ages might have been a lyric poet, the person `` capable of putting together words that stir and move and sing ''.

Thus there is a clearer division of authority, administrative and legislative.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, the need for the B-70 as a strategic weapon system is doubtful.

Thus technical efficiency is achieved at the expense of actual experience.

Thus, there is an added incentive to stay on the job.

Thus, the Span of its ossification was shortened and the center's ability to `` catch up '' in ossification is demonstrated.

Thus T is not diagonalizable.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.

Thus we do not score the number of bull's-eyes, and the random variable is not the number of successes.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.

Thus if the instrument depends on the pressure or suction effect alone, and this pressure or suction is measured against the air pressure in an ordinary room, in which the doors and windows are carefully closed and a newspaper is then burnt up the chimney, an effect may be produced equal to a wind of 10 mi / h ( 16 km / h ); and the opening of a window in rough weather, or the opening of a door, may entirely alter the registration.

Thus the cofinality of a finite partially ordered set is equal to the number of its maximal elements.

) Thus, for example, a 2x6 rectangle and a 3x4 rectangle are equal but not congruent, and the letter R is congruent to its mirror image.

Thus a gallon is equal to four quarts, eight pints, sixteen cups or thirty-two gills.

Thus when there are many molecules in the gas, there will be an equal number moving in one direction as any other hence demonstrating isotropy.

However, a second definition and usage has historically been in practice in many fields of computer science and information technology, which defines the prefix kilo when used with byte or bit units of data as 1024 ( 2 < sup > 10 </ sup >); this is due to the mathematical coincidence that Thus, in these fields 1 kilobyte is equal to 1 kibibyte, a new unit standardized as part of the binary prefixes to resolve the ambiguity.

Thus the total revenue curve for a competitive company is a ray with a slope equal to the market price.

Thus for each unit the seller tries to set the price equal to the consumer ’ s reservation price.

Thus each polynomial is actually equal to the sum of the terms used in its formal expression, if such a term a < sub > i </ sub > X < sup > i </ sup > is interpreted as a polynomial that has zero coefficients at all powers of X other than X < sup > i </ sup >.

Thus nowadays the dominant intuitive idea of the conditions justifying price taking and thus rendering a market perfectly competitive is an amalgam of several different notions, not all present, nor given equal weight, in all treatments.

Thus, the effect of using this procedure is to make activity equal to the numerical value of concentration.

Thus, the average drag ( retarding ) force on the system must equal the average propulsion force on the system.

Thus a net power is released into the electric field equal to the photon energy hν times this net transition rate.

Thus, because all humans have been created equal, they all require equal opportunities and treatment.

Thus either, the cardinality of the reals, is equal to or it is strictly larger.

Thus, Vega has a relatively flat electromagnetic spectrum in the visual region — wavelength range 350 – 850 nanometers, most of which can be seen with the human eye — so the flux densities are roughly equal ; 2000 – 4000 Jy.

Thus, engines with equal power should be compared: a naturally aspirated 1. 3-liter Wankel engine with a naturally aspirated 1. 3-liter four-stroke reciprocating piston engine with equal power.

Its change is equal to the amount of reversible work done on, or obtainable from, a system at constant T. Thus its appellation " work content ", and the designation A from Arbeit, the German word for work.

Thus, Schleiden and Schwann became the first to formulate what was then an informal belief as a principle of biology equal in importance to the atomic theory of chemistry.

Thus, what the axiom is really saying is that two sets are equal if and only if they have precisely the same members.

Thus on 16 January 1968, the Zambian pound was replaced by the kwacha with the new official rate equal to one half the old unit, or US $ 1.