An assembly comprising: a gas turbine engine for a vertical takeoff and landing (VTOL) aircraft, the gas turbine engine comprising: a low pressure spool including a low pressure turbine shaft operatively connected to at least one turbine, the low pressure turbine shaft rotatable about an engine axis; a high pressure spool including at least one high pressure turbine and at least one high pressure compressor operatively connected together by a high pressure shaft and rotatable about the engine axis, the high pressure shaft being independently rotatable relative to the low pressure turbine shaft; a low pressure compressor operatively connected to a low pressure compressor shaft that is independently rotatable relative to the high pressure shaft and the low pressure turbine shaft; and a differential gearbox (30; 130) having an input operatively connected to the low pressure turbine shaft, a first output and a second output, the first output of the differential gearbox (30; 130) operatively connected to the low pressure compressor shaft and the second output of the differential gearbox (30; 130) operatively connected to an output shaft of the gas turbine engine, the differential gearbox (30; 130) permitting the output shaft, the low pressure compressor shaft and the low pressure turbine shaft to rotate at different speeds; and a control system in operative connection with the gas turbine engine, the control system configured to operate the gas turbine engine in a VTOL engine operating configuration or a cruise engine operating configuration, wherein the low pressure compressor includes variable inlet guide vanes, the control system is configured to position the variable inlet guide vanes in a substantially open position when the gas turbine engine is operated by the control system in the VTOL engine operating configuration, and the control system is configured to move the variable inlet guide vanes into a more closed position relative to the substantially open position when the gas turbine engine is operated by the control system in a cruise engine operating configuration. a gas turbine engine for a vertical takeoff and landing (VTOL) aircraft, the gas turbine engine comprising: a low pressure spool including a low pressure turbine shaft operatively connected to at least one turbine, the low pressure turbine shaft rotatable about an engine axis; a high pressure spool including at least one high pressure turbine and at least one high pressure compressor operatively connected together by a high pressure shaft and rotatable about the engine axis, the high pressure shaft being independently rotatable relative to the low pressure turbine shaft; a low pressure compressor operatively connected to a low pressure compressor shaft that is independently rotatable relative to the high pressure shaft and the low pressure turbine shaft; and a differential gearbox (30; 130) having an input operatively connected to the low pressure turbine shaft, a first output and a second output, the first output of the differential gearbox (30; 130) operatively connected to the low pressure compressor shaft and the second output of the differential gearbox (30; 130) operatively connected to an output shaft of the gas turbine engine, the differential gearbox (30; 130) permitting the output shaft, the low pressure compressor shaft and the low pressure turbine shaft to rotate at different speeds; and a low pressure spool including a low pressure turbine shaft operatively connected to at least one turbine, the low pressure turbine shaft rotatable about an engine axis; a high pressure spool including at least one high pressure turbine and at least one high pressure compressor operatively connected together by a high pressure shaft and rotatable about the engine axis, the high pressure shaft being independently rotatable relative to the low pressure turbine shaft; a low pressure compressor operatively connected to a low pressure compressor shaft that is independently rotatable relative to the high pressure shaft and the low pressure turbine shaft; and a differential gearbox (30; 130) having an input operatively connected to the low pressure turbine shaft, a first output and a second output, the first output of the differential gearbox (30; 130) operatively connected to the low pressure compressor shaft and the second output of the differential gearbox (30; 130) operatively connected to an output shaft of the gas turbine engine, the differential gearbox (30; 130) permitting the output shaft, the low pressure compressor shaft and the low pressure turbine shaft to rotate at different speeds; and a control system in operative connection with the gas turbine engine, the control system configured to operate the gas turbine engine in a VTOL engine operating configuration or a cruise engine operating configuration, wherein the low pressure compressor includes variable inlet guide vanes, the control system is configured to position the variable inlet guide vanes in a substantially open position when the gas turbine engine is operated by the control system in the VTOL engine operating configuration, and the control system is configured to move the variable inlet guide vanes into a more closed position relative to the substantially open position when the gas turbine engine is operated by the control system in a cruise engine operating configuration.