Seja y um ângulo medido em graus tal que 0º ≤ y ≤ 180º com y ≠ 90º. Ao multiplicarmos a matriz abaixo por α, sendo α ≠ 0, qual o determinante da matriz resultante?

!$ \begin{bmatrix}\,1\,&\,\mathrm{tg}y\,&\,1\,\\\,\\\,\alpha\,&\,\mathrm{tg}y\,&\,1\,\\\,\\\,\mathrm\,{cos}y\,&\,\mathrm\,{sen}y\,&\,\mathrm\,{cos}\,y\,\end{bmatrix} !$

Quando se faz alguns lados de um polígono tenderem a zero ele degenera naturalmente em um polígono de menor número de lados podendo até eventualmente degenerar em um segmento de reta. Dessa maneira, considere um quadrilátero com duas diagonais iguais e de comprimento !$ 5\sqrt{2} !$ cada uma. Sendo A a área desse quadrilátero, então:

Minister calls for wider flexible working rights

British government ministers are considering giving all employees the right to ask for flexible working hours "from the beginning" of a new job as part of plans to encourage a fundamental shift in working habits.

The Work and Pensions Secretary, Yvette Cooper, says her office is working with employers and organisations such as the federation of small businesses to draw up new ways of supporting men as well as women and non-parents as well as parents working more flexible hours.

The current rules are limited to parents of children under 16 and carers, and Cooper wants to extend them. "You want people to offer flexible working from the beginning and we need to look again at how the legislation can support different ways of doing that," she said.

"There will be some areas where it's not possible to fit round particular school hours or particular things where the nature of the business makes it hard - but what you need is the cultural change for everybody to think differently." Cooper's proposals come as the government announced that fathers will be given the right to six months' paternity leave.

There will be a legal right to take the mother's place at home for the last three months of a nine-month maternity break; they would receive £123 a week in statutory pay. Fathers would then be entitled to take a further three months' unpaid leave. The move was criticised by some business leaders.

(From: The Guardian, Friday 29 January 2010 -slightly adapted)