#### Image of a Line Under Transformation By a Matrix

A matrix is a linear transformation, which means that it sends a line to a line. To find the image of the line on transformation by the matrix we represent the line by the vector and multiply the vector by the matrix: From this we see that (1) (2)...

https://astarmathsandphysics.com/a-level-maths-notes/fp3/3522-image-of-a-line-under-transformation-by-a-matrix.html#### Finding the Equation of the Image of a Curve Under the Reciprocal Function

To find the equation of the image of a path under the reciprocal function Write down an equation relating the and components of all points on Replace by and by (Note that ) Simplify the resulting equation to obtain an equation relating the and...

https://astarmathsandphysics.com/university-maths-notes/complex-analysis/1828-finding-the-equation-of-the-image-of-a-curve-under-the-reciprocal-function.html#### The Image of a Line Under a Transformation Represented by a Matrix

Any transformation represented by a matrix whose entries are numbers is linear. The matrix will send a line to a line. The transformed line will in general be rotated and scaled, but it will still be a line. For example, suppose a transformation is...

https://astarmathsandphysics.com/a-level-maths-notes/fp4/3543-the-image-of-a-line-under-a-transformation-represented-by-a-matrix.html#### The Three Point Trick

The Three Point Trick is a method of finding the equation of the image of a generalized circle – a circle or line (a line can be considered a circle of infinite radius) – after a generalized mobius transformation. Any circle is completely defined by...

https://astarmathsandphysics.com/university-maths-notes/complex-analysis/1884-the-three-point-trick.html#### MRI Scanners

Magnetic resonance imaging (MRI) uses the body's natural magnetic properties to produce high resolution images of the inside of the body. It does this using the properties of the hydrogen ion. The hydrogen proton can be likened to the planet earth,...

https://astarmathsandphysics.com/a-level-physics-notes/medical-physics/2858-mri-scanners.html#### Proof That Projection Mappings From a Plane to a Line Are Continuous With Respect to the Continuous Topology

Define the projection of the point onto the real and axes respectively as Consider the inverse function If acts on an open interval the result is a vertical strip with The set of open intervals is a basis for and the inverse image of each open interval...

https://astarmathsandphysics.com/university-maths-notes/topology/2308-proof-that-projection-mappings-from-a-plane-to-a-line-are-continuous-with-respect-to-the-continuous-topology.html#### Measurement of Wavelength Using a Diffraction Grating and a Spectrometer

Apparatus: Spectrometer, sodium discharge tube with its power supply, diffraction grating, magnifying glass, black cloth light shade. Procedure: (a) Setting up the spectrometer 1. Turn on the sodium lamp (it will take about 5 minutes to fully come on)....

https://astarmathsandphysics.com/a-level-physics-notes/experimental-physics/2706-measurement-of-wavelength-using-a-diffraction-grating-and-a-spectrometer.html#### X - Rays

On 8 November 1895, Willhelm Röntgen, a physicist working at the University of Wurzburg discovered X rays when a photographic plate shut in a draw was found to be exposed when left close to a sample of uranium salt. Röntgen's work provided him with the...

https://astarmathsandphysics.com/a-level-physics-notes/medical-physics/2880-x-rays.html#### Gravitational Lensing

Gravitational lensing occurs when a large galaxy lies between the Earth and some distant object of interest. As this light moves away from the object in the rough direction of the earth, some of it might pass close to the intervening galaxy in such a...

https://astarmathsandphysics.com/a-level-physics-notes/cosmology/2514-gravitational-lensing.html#### Inverse Points and Apollonian Form

An curve expressed as is said to be written in Apollonian form. A curve written in Apollonian form is in fact either a circle or a line – circles and lines together constitute the set of generalized circles, with a line being considered a circle of...

https://astarmathsandphysics.com/university-maths-notes/complex-analysis/1838-inverse-points-and-apollonian-form.html#### Gravity and Spacetime

The Newtonian view of space is a rigid three dimensional structure, which can be expressed as three perpendicular directions. Time is separate from the space dimensions. Time permeates all of space, moving at the same rate everywhere. Gravity in this...

https://astarmathsandphysics.com/ib-physics-notes/relativity/1441-gravity-and-spacetime.html#### Introduction to Metric Spaces

A metric space is a set of points where the distance between any two points can be calculated with a function of the coordinates of the points, called a metric: The metric space which most closely corresponds to our intuitive understanding of space is...

https://astarmathsandphysics.com/university-maths-notes/metric-spaces/1935-introduction-to-metric-spaces.html#### Storing Digital Information

Information is stored digitally on a computer hard disk as a sequence of 0's and 1's. The sequence may encode a piture, sound, text or some other kind of information. Suppose a sound recording to sampled into 8 bits at 1000, 2000, 3000, 4000, 5000 and...

https://astarmathsandphysics.com/a-level-physics-notes/digital-information/2545-storing-digital-information.html#### Summary

1. X-Rays are high-energy EM waves, with λ considerably shorter than light. 2. To produce X-Rays: a. A filament is heated by a low voltage transformer, causing electrons to ‘boil’ off the surface of the filament. b. A high voltage transformer provides...

https://astarmathsandphysics.com/a-level-physics-notes/medical-physics/2864-summary.html

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