Thus 4, 000, 000, which has a logarithm ( in base 10 ) of 6. 602, has 7 as its nearest order of magnitude, because " nearest " implies rounding rather than truncation.

Thus force is a vector quantity, because its effect depends on the direction as well as on the magnitude of the action.

Thus two arrows and in space represent the same free vector if they have the same magnitude and direction: that is, they are equivalent if the quadrilateral ABB ′ A ′ is a parallelogram.

Thus, F (− q ) has the same magnitude as F ( q ) but they have the opposite phase, i. e., φ ( q ) = − φ ( q )

Thus, the efficiency of the process may be increased by many orders of magnitude.

Thus the magnitude of the shift is related not to the Compton wavelength of the electron, but to the Compton wavelength of the entire atom, which can be upwards of 10 000 times smaller.

Thus to find the median, order the list according to its elements ' magnitude and then repeatedly remove the pair consisting of the highest and lowest values until either one or two values are left.

Thus at any place where there is a zero or pole involving the term, the magnitude of that term is.

Thus one will expect to be within 1 / 8 to 8 times the correct value – within an order of magnitude, and much less than the worst case of erring by a factor of ( about 2. 7 orders of magnitude ).

Thus, the magnitude of weight change from loss of air during a dive varies from roughly 4. 3 kg ( 9. 5 lbs ) representing the total air content of a steel 15 litre cylinder at 230 bar / 3500 psi ( in practice, reserve requirements dictate that only about 8 lbs of this will be breathed ), to about 5 lbs difference for the smaller 80 ft < sup > 3 </ sup > aluminum-80 ( AL80 ) tank ( 11. 1 litres internal capacity ) pressurised to 200 bar / 3000 psi, and again assuming that only 5 / 6ths of the air in the tank is used, leaving a typical safety reserve.

Thus, sympathetic responses are often conditional on or their magnitude is determined by the causes of the emotion in the person being sympathized with.

Thus, the pressure on a fluid at rest is isotropic ; i. e., it acts with equal magnitude in all directions.

Thus if an object has apparent magnitude at distance from the observer, then all other things being equal, it will have magnitude at distance.

Thus the order of magnitude for the spin-orbital coupling is.

Thus, for medium-sized earthquakes, the moment magnitude values should be similar to Richter values.

From equation ( 2 ) it follows, since T always has unit magnitude, that N is always perpendicular to T. From equation ( 3 ) it follows that B is always perpendicular to both T and N. Thus, the three unit vectors T, N, and B are all perpendicular to each other.

Thus, magnitude does depend on the extent of the entity or system in the case of extensive quantity.

Thus, if one is at a site where the naked eye limiting magnitude is 5, the telescope will allow one to see stars as faint as about magnitude 13.

Thus those of the 1st magnitude are brighter than those of the 2nd.

) Thus, v is a constant, and the velocity vector v also rotates with constant magnitude v, at the same angular rate ω.

Thus, the magnitude of the kinetic isotope effect can be used to elucidate the reaction mechanism.

Thus if the gyro and platform-controller combination maintains the platform with zero angular deviation about the **yf axis, the system can be rotated with an angular velocity Af if a torque is supplied to the gyro output axis Aj.

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, at a given angular rate of rotation, a concave surface represents the stable situation, and the more rapid the rotation, the more concave this surface.

Thus, this angular arrangement sees a decrease in the net positional entropy of the approaching cylinder ( there are fewer states available to it ).

where θ is the angle between the vectors Ω < sub > P </ sub > and L. Thus, if the gyroscope's spin slows down ( for example, due to friction ), its angular momentum decreases and so the rate of precession increases.

Thus, the time travel mechanism would also have to provide instantaneous teleportation, with infinitely accurate and simultaneous adjustment of final 3D location, linear momentum, and angular momentum.

Thus thermal radiation contains information about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the mass, angular momentum, and charge of the black hole ( the no-hair theorem ).

Thus the corners become rounded, because angular edges provide more than one area of attack by exposing a greater amount of surface area.

Thus, the position of a rigid body has two components: linear and angular, respectively.

Thus, measuring 180 ° along the angular direction you would encounter a half wave, so the mode number in the angular direction is 1.

Thus, angular magnification is given by:

Thus a low DOP value represents a better GPS positional precision due to the wider angular separation between the satellites used to calculate a GPS unit's position.

Thus, the tangent half-angle formulae give conversions between the stereographic coordinate t on the unit circle and the standard angular coordinate φ.

Thus, measurements of this angular scale allow an estimation of Ω < sub > 0 </ sub >.

Thus, in the Kepler problem, the angular momentum of a planet about the sun is conserved and the areal velocity is a vector of constant magnitude perpendicular to the orbital plane.

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 the event duration is determined by the time it takes the apparent motion of the lens in the sky to cover an angular distance.

Thus, any transverse velocity of the emitting source plays no part in aberration.

In the field of high-energy particle physics, the fundamental velocity unit is the speed of light c. Thus, dividing energy in eV by the speed of light in vacuum, one can describe the momentum of an electron in units of eV / c.

Thus, the monetary model predicts that the velocity of money will increase as a result of an excessive increase in the money supply.

Thus a ruler that is one meter long in one frame of reference will not be one meter long in a reference frame that is travelling at a velocity relative to the first frame.

Thus the velocity can be measured from the amount of redshift ( or blueshift ) of the star's spectrum.

Thus, an object starting from rest will attain a velocity of 9. 81 m / s ( 32. 2 ft / s ) after one second, 19. 62 m / s ( 64. 4 ft / s ) after two seconds, and so on, adding 9. 81 m / s ( 32. 2 ft / s ) to each resulting velocity.

This question has two fundamental physical units: time t and length, and three dimensional variables: distance D, time taken T, and velocity V. Thus there is 3 − 2 = 1 dimensionless quantity.

Thus, if V < sub > g </ sup > is the group velocity of a phonon wave packet, then the relaxation length is defined as:

Thus, velocity is the time rate of change of position, and the dot denotes the derivative with respect to time.

Thus, for bodies in pure translation the velocity and acceleration of every point P in the body are given by

Thus, the relative difference in velocity between a source and an observer is what gives rise to the doppler effect.

Thus shot to shot consistency is maintained for longer than in an unregulated rifle, at the expense of efficiency, shots per fill and often at a lower velocity.

Thus, the perturbation introduced to the system is described by a velocity field of infinitesimally small amplitude,.

Thus, in cases of very viscous flows ( e. g. Couette Flow ), the vorticity will be diffused throughout the flow field and it is probably simpler to look at the velocity field ( i. e. vectors of fluid motion ) rather than look at the vorticity field ( i. e. vectors of curl of fluid motion ) which is less intuitive.

Thus if a rocket burst is in the direction of the velocity, in the reversed case it is opposite to the velocity.

Thus, for a subsonic flow to be accelerated to supersonic velocities, the nozzle needs to have a converging section in which the flow is subsonic, a throat, at which the flow velocity is the local speed of sound, and a diverging section with supersonic flow.

Thus, since the velocity of sound is approximately 343 m / s at a normal room temperature of about 25 ° C, the reflecting object must be more than 11. 3 m from the sound source at this temperature for an echo to be heard by a person at the source.

Thus the time-of-flight is used to measure velocity, from which the mass-to-charge ratio can be determined.

Thus specific impulse is a velocity, as opposed to the common usage of the word as the ratio of momentum and weight ( weight would not make much sense in this context ).

Thus, it is the velocity of a reference point fixed to the body.

Thus, in animals with early signs of diabetes-induced neuropathy, C peptide treatment in replacement dosage results in improved peripheral nerve function, as evidenced by increased nerve conduction velocity, increased nerve Na +, K + ATPase activity, and significant amelioration of nerve structural changes.