Question

two tasks of supercomputers and Personal digital assistant might be used to do

Answer 1

Space exploration:
Supercomputers are used to study the origin of the universe, the dark-matters. For these studies scientist use IBM’s powerful supercomputer “Roadrunner” at National Laboratory Los Alamos.

Earthquakes studies :
Supercomputers are used to study the Earthquakes phenomenon. Besides that supercomputers are used for natural resources exploration, like natural gas, petroleum, coal, etc.

Weather forecasting :
Supercomputers are used for weather forecasting, and to study the nature and extent of Hurricanes, Rainfalls, windstorms, etc.

Nuclear weapons testing :
Supercomputers are used to run weapon simulation that can test the Range, accuracy & impact of Nuclear weapons.   
IBM’s Sequoia, in United States
Fujitsu’s K Computer in Japan
IBM’s Mira in United States
IBM’s SuperMUC in Germany
NUDT Tianhe-1A in China