Problem: Current circulating in one antenna generally induces a voltage across the feedpoint of nearby antennas or antenna elements. The mathematics presented below are useful in analyzing the electrical behaviour of antenna arrays, where the properties of the individual array elements (such as half wave dipoles) are already known. If those elements were widely separated and driven in a certain amplitude and phase, then each would act independently as that element is known to. However, because of the mutual interaction between their electric and magnetic fields due to proximity, the currents in each element are not simply a function of the applied voltage (according to its driving point impedance), but depend on the currents in the other nearby elements. Note that this now is a near field phenomenon which could not be properly accounted for using the Friis transmission equation for instance.
What are the mathmatic useful towards?
---
Answer: electrical behaviour


Problem: Madonna was criticized for her performance of "Like a Virgin" at the first 1984 MTV Video Music Awards (VMA). She appeared on stage atop a giant wedding cake, wearing a wedding dress and white gloves. The performance is noted by MTV as an iconic moment in VMA history. In later years, Madonna commented that she was terrified of the performance. The next hit was "Material Girl" promoted by her video, a mimicry of Marilyn Monroe's performance of the song "Diamonds Are a Girl's Best Friend" from the 1953 film Gentlemen Prefer Blondes. While filming this video, Madonna started dating actor Sean Penn. They married on her birthday in 1985. Like a Virgin was certified diamond by the Recording Industry Association of America and sold more than 25 million copies worldwide. In February 1984, according to the film director Sir Richard Attenborough, Madonna auditioned at the Royale Theatre on Broadway for a dance role in his movie version of A Chorus Line using her birth-name of Ciccone, but he rejected her.
When did Madonna audition for a dance role in the show "A Chorus Line?" 
---
Answer: February 1984


Problem: Solar distillation can be used to make saline or brackish water potable. The first recorded instance of this was by 16th-century Arab alchemists. A large-scale solar distillation project was first constructed in 1872 in the Chilean mining town of Las Salinas. The plant, which had solar collection area of 4,700 m2 (51,000 sq ft), could produce up to 22,700 L (5,000 imp gal; 6,000 US gal) per day and operate for 40 years. Individual still designs include single-slope, double-slope (or greenhouse type), vertical, conical, inverted absorber, multi-wick, and multiple effect. These stills can operate in passive, active, or hybrid modes. Double-slope stills are the most economical for decentralized domestic purposes, while active multiple effect units are more suitable for large-scale applications.
In what year was a large scale solar distillation project constructed in Las Salinas?
---
Answer:
1872