Maths and physics

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Across
  1. 1. Unit of sound level.
  2. 5. Unit of frequency equal to one event or cycle per second.
  3. 7. A variant of a particular chemical element which differs in neutron number.
  4. 8. A mathematical statement or hypothesis which has been proved on the basis of previously established _______ and previously accepted axioms, effectively the proof of the truth of a statement or expression.
  5. 9. The study of the formal laws of reasoning.
  6. 10. The act of squaring, or finding a square equal in area to a given figure, or finding the area of a geometrical figure or the area under a curve (such as by a process of numerical integration).
  7. 11. A number which, when multiplied by x yields the multiplicative identity 1, and can therefore be thought of as the inverse of multiplication, e.g. the _______ of x is 1⁄x .
  8. 12. Ratio of output work to input work.
  9. 14. It is a massive and extremely remote celestial object, emitting exceptionally large amounts of energy, and typically having a starlike image in a telescope. It has been suggested that _____ contain massive black holes and may represent a stage in the evolution of some galaxies.
  10. 15. Change from liquid to vapor state.
  11. 17. It is an elementary particle and a fundamental constituent of matter, the main constituent of a proton.
  12. 20. An ordered set whose elements are usually determined based on some function of the counting numbers, e.g. an arithmetic ______ is a set where each element is the previous element plus or minus a number.
  13. 21. Small quantities of material added to semiconductor to increase electrical conduction.
  14. 23. Unit of luminous intensity.
Down
  1. 2. A member of, or an object in, a set.
  2. 3. A proposition that is not actually proved or demonstrated, but is considered to be self-evident and universally accepted as a starting point for deducing and inferring other truths and theorems, without any need of proof.
  3. 4. The part of mathematics concerned with the size, shape and relative position of figures, or the study of lines, angles, shapes and their properties.
  4. 6. A physical quantity having magnitude and direction, represented by a directed arrow indicating its orientation in space.
  5. 9. The point towards which a series or function converges.
  6. 10. A number system that extends complex numbers to four dimensions (so that an object is described by a real number and three complex numbers, all mutually perpendicular to each other), which can be used to represent a three-dimensional rotation by just an angle and a vector.
  7. 13. A rectangular array of numbers, which can be added, subtracted and multiplied, and used to represent linear transformations and vectors, solve equations, etc.
  8. 16. Device used to receive or transmit electromagnetic waves.
  9. 18. Closeness of a measurement to the standard value of that quantity.
  10. 19. Product of force and time interval over which it acts.
  11. 22. The steepness or incline of a line, determined by reference to two points on the line.